id	sid	tid	token	lemma	pos
ma-51	1	1	2022	2022	NUM
ma-51	1	2	ada	ada	PROPN
ma-51	1	3	academica	academica	PROPN
ma-51	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-51	1	5	.	.	PUNCT
ma-51	2	1	j.	j.	PROPN
ma-51	2	2	math	math	PROPN
ma-51	2	3	.	.	PUNCT
ma-51	3	1	anal	anal	ADJ
ma-51	3	2	.	.	PUNCT
ma-51	3	3	2	2	NUM
ma-51	3	4	(	(	PUNCT
ma-51	3	5	2022	2022	NUM
ma-51	3	6	)	)	PUNCT
ma-51	3	7	10doi	10doi	NUM
ma-51	3	8	:	:	PUNCT
ma-51	3	9	10.28924	10.28924	NUM
ma-51	3	10	/	/	SYM
ma-51	3	11	ada	ada	PROPN
ma-51	3	12	/	/	SYM
ma-51	3	13	ma.2.10	ma.2.10	PROPN
ma-51	3	14	weak	weak	ADJ
ma-51	3	15	and	and	CCONJ
ma-51	3	16	strong	strong	ADJ
ma-51	3	17	convergence	convergence	NOUN
ma-51	3	18	theorems	theorem	NOUN
ma-51	3	19	of	of	ADP
ma-51	3	20	modified	modified	ADJ
ma-51	3	21	projection	projection	NOUN
ma-51	3	22	-	-	PUNCT
ma-51	3	23	type	type	NOUN
ma-51	3	24	ishikawa	ishikawa	PROPN
ma-51	3	25	iteration	iteration	NOUN
ma-51	3	26	scheme	scheme	NOUN
ma-51	3	27	for	for	ADP
ma-51	3	28	lipschitz	lipschitz	NOUN
ma-51	3	29	α	α	PRON
ma-51	3	30	-	-	PUNCT
ma-51	3	31	hemicontractive	hemicontractive	ADJ
ma-51	3	32	mappings	mapping	NOUN
ma-51	3	33	imo	imo	PROPN
ma-51	3	34	kalu	kalu	PROPN
ma-51	3	35	agwu∗	agwu∗	NOUN
ma-51	3	36	,	,	PUNCT
ma-51	3	37	donatus	donatus	X
ma-51	3	38	ikechi	ikechi	PROPN
ma-51	3	39	igbokwe	igbokwe	PROPN
ma-51	3	40	department	department	PROPN
ma-51	3	41	of	of	ADP
ma-51	3	42	mathematics	mathematic	NOUN
ma-51	3	43	,	,	PUNCT
ma-51	3	44	micheal	micheal	NOUN
ma-51	3	45	okpara	okpara	NOUN
ma-51	3	46	university	university	PROPN
ma-51	3	47	of	of	ADP
ma-51	3	48	agriculture	agriculture	PROPN
ma-51	3	49	,	,	PUNCT
ma-51	3	50	umudike	umudike	NOUN
ma-51	3	51	,	,	PUNCT
ma-51	3	52	umuahia	umuahia	PROPN
ma-51	3	53	abia	abia	PROPN
ma-51	3	54	state	state	PROPN
ma-51	3	55	,	,	PUNCT
ma-51	3	56	nigeria	nigeria	PROPN
ma-51	3	57	agwuimo@gmail.com	agwuimo@gmail.com	PROPN
ma-51	3	58	,	,	PUNCT
ma-51	3	59	igbokwedi@yahoo.com	igbokwedi@yahoo.com	X
ma-51	4	1	∗correspondence	∗correspondence	NOUN
ma-51	4	2	:	:	PUNCT
ma-51	4	3	agwuimo@gmail.com	agwuimo@gmail.com	X
ma-51	4	4	abstract	abstract	ADJ
ma-51	4	5	.	.	PUNCT
ma-51	5	1	in	in	ADP
ma-51	5	2	this	this	DET
ma-51	5	3	paper	paper	NOUN
ma-51	5	4	,	,	PUNCT
ma-51	5	5	we	we	PRON
ma-51	5	6	establish	establish	VERB
ma-51	5	7	weak	weak	ADJ
ma-51	5	8	and	and	CCONJ
ma-51	5	9	strong	strong	ADJ
ma-51	5	10	convergence	convergence	NOUN
ma-51	5	11	theorems	theorem	NOUN
ma-51	5	12	of	of	ADP
ma-51	5	13	a	a	DET
ma-51	5	14	two	two	NUM
ma-51	5	15	-	-	PUNCT
ma-51	5	16	step	step	NOUN
ma-51	5	17	modifiedprojection	modifiedprojection	NOUN
ma-51	5	18	-	-	PUNCT
ma-51	5	19	type	type	NOUN
ma-51	5	20	ishikawa	ishikawa	PROPN
ma-51	5	21	iterative	iterative	NOUN
ma-51	5	22	scheme	scheme	NOUN
ma-51	5	23	to	to	ADP
ma-51	5	24	the	the	DET
ma-51	5	25	fixed	fix	VERB
ma-51	5	26	point	point	NOUN
ma-51	5	27	of	of	ADP
ma-51	5	28	α	α	NOUN
ma-51	5	29	-	-	ADJ
ma-51	5	30	hemicontractive	hemicontractive	ADJ
ma-51	5	31	mappings	mapping	NOUN
ma-51	5	32	withoutany	withoutany	VERB
ma-51	5	33	compactness	compactness	NOUN
ma-51	5	34	assumption	assumption	NOUN
ma-51	5	35	on	on	ADP
ma-51	5	36	the	the	DET
ma-51	5	37	operator	operator	NOUN
ma-51	5	38	or	or	CCONJ
ma-51	5	39	the	the	DET
ma-51	5	40	space	space	NOUN
ma-51	5	41	.	.	PUNCT
ma-51	6	1	our	our	PRON
ma-51	6	2	results	result	NOUN
ma-51	6	3	extend	extend	VERB
ma-51	6	4	,	,	PUNCT
ma-51	6	5	improve	improve	VERB
ma-51	6	6	and	and	CCONJ
ma-51	6	7	generalizeseveral	generalizeseveral	ADJ
ma-51	6	8	previously	previously	ADV
ma-51	6	9	known	know	VERB
ma-51	6	10	results	result	NOUN
ma-51	6	11	of	of	ADP
ma-51	6	12	the	the	DET
ma-51	6	13	existing	exist	VERB
ma-51	6	14	literature	literature	NOUN
ma-51	6	15	.	.	PUNCT
ma-51	7	1	1	1	X
ma-51	7	2	.	.	X
ma-51	7	3	introduction	introduction	NOUN
ma-51	7	4	let	let	VERB
ma-51	7	5	h	h	PRON
ma-51	7	6	be	be	AUX
ma-51	7	7	a	a	DET
ma-51	7	8	real	real	ADJ
ma-51	7	9	hilbert	hilbert	NOUN
ma-51	7	10	space	space	NOUN
ma-51	7	11	with	with	ADP
ma-51	7	12	inner	inner	ADJ
ma-51	7	13	product	product	NOUN
ma-51	7	14	〈	〈	PROPN
ma-51	7	15	,	,	PUNCT
ma-51	7	16	.	.	PUNCT
ma-51	8	1	,	,	PUNCT
ma-51	8	2	〉	〉	NOUN
ma-51	8	3	and	and	CCONJ
ma-51	8	4	induced	induce	VERB
ma-51	8	5	norm	norm	NOUN
ma-51	8	6	‖	‖	ADJ
ma-51	8	7	,	,	PUNCT
ma-51	8	8	.	.	PUNCT
ma-51	8	9	,	,	PUNCT
ma-51	8	10	‖	‖	PROPN
ma-51	8	11	,	,	PUNCT
ma-51	8	12	k	k	PROPN
ma-51	8	13	a	a	DET
ma-51	8	14	nonemptyconvex	nonemptyconvex	ADJ
ma-51	8	15	and	and	CCONJ
ma-51	8	16	closed	closed	ADJ
ma-51	8	17	subset	subset	NOUN
ma-51	8	18	of	of	ADP
ma-51	8	19	h	h	PROPN
ma-51	8	20	and	and	CCONJ
ma-51	8	21	t	t	PROPN
ma-51	8	22	:	:	PUNCT
ma-51	9	1	k	k	X
ma-51	9	2	−→	−→	NOUN
ma-51	9	3	k	k	PROPN
ma-51	9	4	a	a	DET
ma-51	9	5	selfmap	selfmap	NOUN
ma-51	9	6	on	on	ADP
ma-51	9	7	k.	k.	NOUN
ma-51	9	8	we	we	PRON
ma-51	9	9	use	use	VERB
ma-51	9	10	f	f	PROPN
ma-51	9	11	(	(	PUNCT
ma-51	9	12	t	t	PROPN
ma-51	9	13	)	)	PUNCT
ma-51	9	14	to	to	PART
ma-51	9	15	denote	denote	VERB
ma-51	9	16	the	the	DET
ma-51	9	17	setof	setof	NOUN
ma-51	9	18	fixed	fix	VERB
ma-51	9	19	point	point	NOUN
ma-51	9	20	of	of	ADP
ma-51	9	21	t	t	PROPN
ma-51	9	22	,	,	PUNCT
ma-51	9	23	n	n	CCONJ
ma-51	9	24	to	to	PART
ma-51	9	25	denote	denote	VERB
ma-51	9	26	the	the	DET
ma-51	9	27	set	set	NOUN
ma-51	9	28	of	of	ADP
ma-51	9	29	natural	natural	ADJ
ma-51	9	30	numbers	number	NOUN
ma-51	9	31	and	and	CCONJ
ma-51	9	32	xn	xn	PROPN
ma-51	9	33	→	→	SYM
ma-51	9	34	x	x	SYM
ma-51	9	35	(	(	PUNCT
ma-51	9	36	respectively	respectively	ADV
ma-51	9	37	xn	xn	NUM
ma-51	9	38	⇀	⇀	NUM
ma-51	9	39	x	x	X
ma-51	9	40	)	)	PUNCT
ma-51	9	41	todenote	todenote	VERB
ma-51	9	42	the	the	DET
ma-51	9	43	strong	strong	ADJ
ma-51	9	44	(	(	PUNCT
ma-51	9	45	weak	weak	ADJ
ma-51	9	46	)	)	PUNCT
ma-51	9	47	convergence	convergence	NOUN
ma-51	9	48	of	of	ADP
ma-51	9	49	the	the	DET
ma-51	9	50	sequence	sequence	NOUN
ma-51	9	51	{	{	PUNCT
ma-51	9	52	xn}∞n=0	xn}∞n=0	NUM
ma-51	9	53	to	to	ADP
ma-51	9	54	the	the	DET
ma-51	9	55	point	point	NOUN
ma-51	9	56	x	x	X
ma-51	9	57	.	.	PUNCT
ma-51	10	1	definition	definition	NOUN
ma-51	10	2	1.1	1.1	NUM
ma-51	10	3	.	.	PUNCT
ma-51	11	1	let	let	VERB
ma-51	11	2	t	t	NOUN
ma-51	11	3	:	:	PUNCT
ma-51	11	4	k	k	PROPN
ma-51	11	5	−→	−→	NOUN
ma-51	11	6	k	k	PROPN
ma-51	11	7	be	be	AUX
ma-51	11	8	a	a	DET
ma-51	11	9	maaping	maaping	NOUN
ma-51	11	10	.	.	PUNCT
ma-51	12	1	then	then	ADV
ma-51	12	2	i.	i.	PROPN
ma-51	12	3	t	t	PROPN
ma-51	12	4	is	be	AUX
ma-51	12	5	said	say	VERB
ma-51	12	6	to	to	PART
ma-51	12	7	be	be	AUX
ma-51	12	8	l	l	NOUN
ma-51	12	9	-	-	NOUN
ma-51	12	10	lipschitizian	lipschitizian	ADJ
ma-51	12	11	if	if	SCONJ
ma-51	12	12	there	there	PRON
ma-51	12	13	exists	exist	VERB
ma-51	12	14	l	l	NOUN
ma-51	12	15	>	>	X
ma-51	12	16	0	0	NUM
ma-51	12	17	such	such	ADJ
ma-51	12	18	that	that	SCONJ
ma-51	12	19	‖ts	‖ts	NUM
ma-51	12	20	−	−	NOUN
ma-51	12	21	tz‖	tz‖	NOUN
ma-51	12	22	≤	≤	ADV
ma-51	12	23	‖s	‖s	ADJ
ma-51	13	1	−	−	PROPN
ma-51	13	2	z‖,∀s	z‖,∀	NOUN
ma-51	13	3	,	,	PUNCT
ma-51	13	4	z	z	PROPN
ma-51	13	5	∈	∈	PROPN
ma-51	13	6	k.	k.	PROPN
ma-51	13	7	(	(	PUNCT
ma-51	13	8	1.1	1.1	NUM
ma-51	13	9	)	)	PUNCT
ma-51	13	10	from	from	ADP
ma-51	13	11	the	the	DET
ma-51	13	12	definition	definition	NOUN
ma-51	13	13	,	,	PUNCT
ma-51	13	14	it	it	PRON
ma-51	13	15	easy	easy	ADJ
ma-51	13	16	to	to	PART
ma-51	13	17	observe	observe	VERB
ma-51	13	18	that	that	SCONJ
ma-51	13	19	every	every	DET
ma-51	13	20	nonexpansive	nonexpansive	ADJ
ma-51	13	21	mapping	mapping	NOUN
ma-51	13	22	is	be	AUX
ma-51	13	23	lipschitizian	lipschitizian	ADJ
ma-51	13	24	with	with	ADP
ma-51	13	25	l	l	NOUN
ma-51	13	26	=	=	SYM
ma-51	13	27	1	1	X
ma-51	13	28	.	.	X
ma-51	13	29	ii	ii	PROPN
ma-51	13	30	.	.	PUNCT
ma-51	14	1	t	t	PROPN
ma-51	14	2	is	be	AUX
ma-51	14	3	called	call	VERB
ma-51	14	4	k	k	NOUN
ma-51	14	5	-	-	PUNCT
ma-51	14	6	strictly	strictly	ADV
ma-51	14	7	pseudocontraction	pseudocontraction	NOUN
ma-51	14	8	(	(	PUNCT
ma-51	14	9	see	see	VERB
ma-51	14	10	,	,	PUNCT
ma-51	14	11	for	for	ADP
ma-51	14	12	example	example	NOUN
ma-51	14	13	,	,	PUNCT
ma-51	14	14	[	[	X
ma-51	14	15	9	9	NUM
ma-51	14	16	]	]	SYM
ma-51	14	17	)	)	PUNCT
ma-51	14	18	if	if	SCONJ
ma-51	14	19	there	there	PRON
ma-51	14	20	exists	exist	VERB
ma-51	14	21	k	k	PROPN
ma-51	14	22	∈	∈	PROPN
ma-51	14	23	(	(	PUNCT
ma-51	14	24	0	0	NUM
ma-51	14	25	,	,	PUNCT
ma-51	14	26	1	1	NUM
ma-51	14	27	]	]	PUNCT
ma-51	14	28	such	such	ADJ
ma-51	14	29	that	that	SCONJ
ma-51	14	30	for	for	ADP
ma-51	14	31	all	all	DET
ma-51	14	32	s	s	NOUN
ma-51	14	33	,	,	PUNCT
ma-51	14	34	z	z	PROPN
ma-51	14	35	∈	∈	PROPN
ma-51	14	36	k	k	NOUN
ma-51	14	37	,	,	PUNCT
ma-51	14	38	the	the	DET
ma-51	14	39	inequality	inequality	NOUN
ma-51	14	40	‖ts	‖ts	NUM
ma-51	14	41	−	−	NOUN
ma-51	14	42	tz‖2	tz‖2	VERB
ma-51	14	43	≤	≤	NUM
ma-51	14	44	‖s	‖s	ADJ
ma-51	14	45	−	−	NOUN
ma-51	14	46	z‖2	z‖2	NOUN
ma-51	14	47	+	+	CCONJ
ma-51	14	48	k‖(i	k‖(i	NOUN
ma-51	14	49	−	−	PROPN
ma-51	14	50	t	t	NOUN
ma-51	14	51	)	)	PUNCT
ma-51	14	52	s	s	PART
ma-51	14	53	−	−	PROPN
ma-51	15	1	(	(	PUNCT
ma-51	15	2	i	i	PRON
ma-51	15	3	−	−	PROPN
ma-51	15	4	t	t	NOUN
ma-51	15	5	)	)	PUNCT
ma-51	15	6	z‖2	z‖2	NOUN
ma-51	15	7	(	(	PUNCT
ma-51	15	8	1.2	1.2	NUM
ma-51	15	9	)	)	PUNCT
ma-51	15	10	hods	hod	NOUN
ma-51	15	11	.	.	PUNCT
ma-51	16	1	note	note	VERB
ma-51	16	2	that	that	SCONJ
ma-51	16	3	if	if	SCONJ
ma-51	16	4	k	k	PROPN
ma-51	16	5	=	=	SYM
ma-51	16	6	1	1	NUM
ma-51	16	7	in	in	ADP
ma-51	16	8	(	(	PUNCT
ma-51	16	9	1.2	1.2	NUM
ma-51	16	10	)	)	PUNCT
ma-51	16	11	,	,	PUNCT
ma-51	16	12	then	then	ADV
ma-51	16	13	t	t	PROPN
ma-51	16	14	is	be	AUX
ma-51	16	15	a	a	DET
ma-51	16	16	pseudocontraction	pseudocontraction	NOUN
ma-51	16	17	.	.	PUNCT
ma-51	17	1	it	it	PRON
ma-51	17	2	well	well	ADV
ma-51	17	3	-	-	PUNCT
ma-51	17	4	known	know	VERB
ma-51	17	5	that	that	SCONJ
ma-51	17	6	in	in	ADP
ma-51	17	7	real	real	ADJ
ma-51	17	8	hilbert	hilbert	NOUN
ma-51	17	9	spaces	space	NOUN
ma-51	17	10	,	,	PUNCT
ma-51	17	11	the	the	DET
ma-51	17	12	class	class	NOUN
ma-51	17	13	of	of	ADP
ma-51	17	14	nonexpansive	nonexpansive	ADJ
ma-51	17	15	mapping	mapping	NOUN
ma-51	17	16	is	be	AUX
ma-51	17	17	a	a	DET
ma-51	17	18	proper	proper	ADJ
ma-51	17	19	subclass	subclass	NOUN
ma-51	17	20	of	of	ADP
ma-51	17	21	the	the	DET
ma-51	17	22	class	class	NOUN
ma-51	17	23	of	of	ADP
ma-51	17	24	received	receive	VERB
ma-51	17	25	:	:	PUNCT
ma-51	17	26	1	1	NUM
ma-51	17	27	nov	nov	PROPN
ma-51	17	28	2021	2021	NUM
ma-51	17	29	.	.	PUNCT
ma-51	18	1	key	key	ADJ
ma-51	18	2	words	word	NOUN
ma-51	18	3	and	and	CCONJ
ma-51	18	4	phrases	phrase	NOUN
ma-51	18	5	.	.	PUNCT
ma-51	19	1	strong	strong	ADJ
ma-51	19	2	convergence	convergence	NOUN
ma-51	19	3	;	;	PUNCT
ma-51	19	4	modified	modify	VERB
ma-51	19	5	ishikawa	ishikawa	PROPN
ma-51	19	6	iterative	iterative	NOUN
ma-51	19	7	scheme	scheme	NOUN
ma-51	19	8	;	;	PUNCT
ma-51	19	9	weak	weak	ADJ
ma-51	19	10	convergence	convergence	NOUN
ma-51	19	11	;	;	PUNCT
ma-51	19	12	α	α	X
ma-51	19	13	-	-	PUNCT
ma-51	19	14	hemicontractive	hemicontractive	ADJ
ma-51	19	15	operator	operator	NOUN
ma-51	19	16	;	;	PUNCT
ma-51	19	17	fixed	fix	VERB
ma-51	19	18	point	point	NOUN
ma-51	19	19	;	;	PUNCT
ma-51	19	20	real	real	ADJ
ma-51	19	21	hilbert	hilbert	NOUN
ma-51	19	22	space	space	NOUN
ma-51	19	23	.	.	PUNCT
ma-51	20	1	1	1	NUM
ma-51	20	2	https://adac.ee	https://adac.ee	PROPN
ma-51	20	3	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	20	4	eur	eur	PROPN
ma-51	20	5	.	.	PUNCT
ma-51	21	1	j.	j.	PROPN
ma-51	21	2	math	math	PROPN
ma-51	21	3	.	.	PUNCT
ma-51	22	1	anal	anal	PROPN
ma-51	22	2	.	.	PUNCT
ma-51	23	1	10.28924	10.28924	NUM
ma-51	23	2	/	/	SYM
ma-51	23	3	ada	ada	PROPN
ma-51	23	4	/	/	SYM
ma-51	23	5	ma.2.10	ma.2.10	PROPN
ma-51	23	6	2	2	NUM
ma-51	23	7	k	k	X
ma-51	23	8	-	-	PUNCT
ma-51	23	9	strictly	strictly	ADV
ma-51	23	10	pseudocontive	pseudocontive	ADJ
ma-51	23	11	mapping	mapping	NOUN
ma-51	23	12	.	.	PUNCT
ma-51	24	1	also	also	ADV
ma-51	24	2	,	,	PUNCT
ma-51	24	3	the	the	DET
ma-51	24	4	class	class	NOUN
ma-51	24	5	of	of	ADP
ma-51	24	6	k	k	PROPN
ma-51	24	7	-	-	PUNCT
ma-51	24	8	strictly	strictly	ADV
ma-51	24	9	pseudocontive	pseudocontive	ADJ
ma-51	24	10	mapping	mapping	NOUN
ma-51	24	11	is	be	AUX
ma-51	24	12	a	a	DET
ma-51	24	13	proper	proper	ADJ
ma-51	24	14	subclass	subclass	NOUN
ma-51	24	15	of	of	ADP
ma-51	24	16	the	the	DET
ma-51	24	17	class	class	NOUN
ma-51	24	18	of	of	ADP
ma-51	24	19	pseudocontive	pseudocontive	ADJ
ma-51	24	20	mapping	mapping	NOUN
ma-51	24	21	.	.	PUNCT
ma-51	25	1	iii	iii	X
ma-51	25	2	.	.	PUNCT
ma-51	25	3	t	t	PROPN
ma-51	25	4	is	be	AUX
ma-51	25	5	called	call	VERB
ma-51	25	6	demicontractive	demicontractive	ADJ
ma-51	25	7	mapping	mapping	NOUN
ma-51	25	8	(	(	PUNCT
ma-51	25	9	see	see	VERB
ma-51	25	10	,	,	PUNCT
ma-51	25	11	for	for	ADP
ma-51	25	12	example	example	NOUN
ma-51	25	13	,	,	PUNCT
ma-51	25	14	[	[	X
ma-51	25	15	?	?	X
ma-51	25	16	]	]	X
ma-51	25	17	)	)	PUNCT
ma-51	25	18	if	if	SCONJ
ma-51	25	19	f	f	PROPN
ma-51	25	20	(	(	PUNCT
ma-51	25	21	t	t	PROPN
ma-51	25	22	)	)	PUNCT
ma-51	25	23	=	=	PRON
ma-51	26	1	{	{	PUNCT
ma-51	26	2	x	x	PUNCT
ma-51	26	3	∈	∈	PROPN
ma-51	26	4	k	k	NOUN
ma-51	26	5	:	:	PUNCT
ma-51	26	6	x	x	X
ma-51	26	7	=	=	SYM
ma-51	26	8	tx	tx	PROPN
ma-51	26	9	}	}	PUNCT
ma-51	26	10	6=	6=	ADP
ma-51	26	11	∅	∅	NOUN
ma-51	26	12	and	and	CCONJ
ma-51	26	13	∀(s	∀(s	NUM
ma-51	26	14	×	×	PROPN
ma-51	26	15	q	q	NOUN
ma-51	26	16	)	)	PUNCT
ma-51	26	17	∈	∈	PROPN
ma-51	26	18	(	(	PUNCT
ma-51	26	19	k	k	PROPN
ma-51	26	20	×	×	PROPN
ma-51	26	21	f	f	X
ma-51	26	22	(	(	PUNCT
ma-51	26	23	t	t	PROPN
ma-51	26	24	)	)	PUNCT
ma-51	26	25	)	)	PUNCT
ma-51	27	1	,	,	PUNCT
ma-51	27	2	there	there	PRON
ma-51	27	3	exists	exist	VERB
ma-51	27	4	k	k	PROPN
ma-51	27	5	∈	∈	PROPN
ma-51	28	1	[	[	X
ma-51	28	2	0	0	NUM
ma-51	28	3	,	,	PUNCT
ma-51	28	4	1	1	NUM
ma-51	28	5	)	)	PUNCT
ma-51	28	6	such	such	ADJ
ma-51	28	7	that	that	SCONJ
ma-51	28	8	the	the	DET
ma-51	28	9	inequality	inequality	NOUN
ma-51	28	10	‖ts	‖ts	NUM
ma-51	28	11	−	−	NOUN
ma-51	28	12	tq‖2	tq‖2	PROPN
ma-51	28	13	≤	≤	NUM
ma-51	28	14	‖s	‖s	ADJ
ma-51	28	15	−	−	PROPN
ma-51	29	1	q‖2	q‖2	NOUN
ma-51	29	2	+	+	CCONJ
ma-51	29	3	k‖s	k‖	NOUN
ma-51	29	4	−	−	PROPN
ma-51	29	5	ts‖2	ts‖2	PROPN
ma-51	29	6	(	(	PUNCT
ma-51	29	7	1.3	1.3	NUM
ma-51	29	8	)	)	PUNCT
ma-51	29	9	hods	hod	NOUN
ma-51	29	10	.	.	PUNCT
ma-51	30	1	iv	iv	X
ma-51	30	2	.	.	PUNCT
ma-51	30	3	t	t	PROPN
ma-51	30	4	is	be	AUX
ma-51	30	5	said	say	VERB
ma-51	30	6	to	to	PART
ma-51	30	7	satisfy	satisfy	VERB
ma-51	30	8	condition	condition	NOUN
ma-51	30	9	a	a	DET
ma-51	30	10	(	(	PUNCT
ma-51	30	11	see	see	VERB
ma-51	30	12	,	,	PUNCT
ma-51	30	13	for	for	ADP
ma-51	30	14	example	example	NOUN
ma-51	30	15	[	[	X
ma-51	30	16	?	?	X
ma-51	30	17	]	]	X
ma-51	30	18	)	)	PUNCT
ma-51	31	1	f	f	PROPN
ma-51	31	2	(	(	PUNCT
ma-51	31	3	t	t	PROPN
ma-51	31	4	)	)	PUNCT
ma-51	31	5	=	=	PRON
ma-51	32	1	{	{	PUNCT
ma-51	32	2	x	x	PUNCT
ma-51	32	3	∈	∈	PROPN
ma-51	32	4	k	k	NOUN
ma-51	32	5	:	:	PUNCT
ma-51	32	6	x	x	X
ma-51	32	7	=	=	SYM
ma-51	32	8	tx	tx	PROPN
ma-51	32	9	}	}	PUNCT
ma-51	32	10	6=	6=	ADP
ma-51	32	11	∅	∅	NOUN
ma-51	32	12	and	and	CCONJ
ma-51	32	13	there	there	PRON
ma-51	32	14	exists	exist	VERB
ma-51	32	15	λ	λ	PROPN
ma-51	32	16	>	>	X
ma-51	32	17	0	0	NUM
ma-51	33	1	such	such	ADJ
ma-51	33	2	that	that	SCONJ
ma-51	33	3	〈	〈	PROPN
ma-51	33	4	s	s	PART
ma-51	33	5	−	−	NOUN
ma-51	33	6	ts	ts	NOUN
ma-51	33	7	,	,	PUNCT
ma-51	33	8	s	s	PART
ma-51	33	9	−	−	PROPN
ma-51	33	10	q	q	PROPN
ma-51	33	11	〉	〉	PROPN
ma-51	33	12	≥	≥	NOUN
ma-51	33	13	λ‖s	λ‖s	PROPN
ma-51	33	14	−	−	PROPN
ma-51	33	15	ts‖2,∀(s	ts‖2,∀(s	NOUN
ma-51	33	16	×	×	PROPN
ma-51	33	17	q	q	NOUN
ma-51	33	18	)	)	PUNCT
ma-51	33	19	∈	∈	PROPN
ma-51	33	20	(	(	PUNCT
ma-51	33	21	k	k	PROPN
ma-51	33	22	×	×	PROPN
ma-51	33	23	f	f	X
ma-51	33	24	(	(	PUNCT
ma-51	33	25	t	t	PROPN
ma-51	33	26	)	)	PUNCT
ma-51	33	27	)	)	PUNCT
ma-51	33	28	.	.	PUNCT
ma-51	34	1	(	(	PUNCT
ma-51	34	2	1.4	1.4	NUM
ma-51	34	3	)	)	PUNCT
ma-51	34	4	it	it	PRON
ma-51	34	5	is	be	AUX
ma-51	34	6	worthy	worthy	ADJ
ma-51	34	7	to	to	PART
ma-51	34	8	mention	mention	VERB
ma-51	34	9	that	that	SCONJ
ma-51	34	10	the	the	DET
ma-51	34	11	class	class	NOUN
ma-51	34	12	of	of	ADP
ma-51	34	13	k	k	PROPN
ma-51	34	14	-	-	PUNCT
ma-51	34	15	strictly	strictly	ADV
ma-51	34	16	pseudocontions	pseudocontion	NOUN
ma-51	34	17	with	with	ADP
ma-51	34	18	a	a	DET
ma-51	34	19	nonempty	nonempty	ADV
ma-51	34	20	fixed	fix	VERB
ma-51	34	21	point	point	NOUN
ma-51	34	22	set	set	NOUN
ma-51	34	23	is	be	AUX
ma-51	34	24	a	a	DET
ma-51	34	25	proper	proper	ADJ
ma-51	34	26	subclass	subclass	NOUN
ma-51	34	27	of	of	ADP
ma-51	34	28	the	the	DET
ma-51	34	29	class	class	NOUN
ma-51	34	30	demicontractions	demicontraction	NOUN
ma-51	34	31	.	.	PUNCT
ma-51	35	1	t	t	PROPN
ma-51	35	2	is	be	AUX
ma-51	35	3	called	call	VERB
ma-51	35	4	hemicontraction	hemicontraction	NOUN
ma-51	35	5	(	(	PUNCT
ma-51	35	6	see	see	VERB
ma-51	35	7	,	,	PUNCT
ma-51	35	8	for	for	ADP
ma-51	35	9	example	example	NOUN
ma-51	35	10	,	,	PUNCT
ma-51	35	11	[	[	X
ma-51	35	12	17	17	NUM
ma-51	35	13	]	]	SYM
ma-51	35	14	)	)	PUNCT
ma-51	35	15	if	if	SCONJ
ma-51	35	16	k	k	PROPN
ma-51	35	17	=	=	NOUN
ma-51	35	18	1	1	NUM
ma-51	35	19	in	in	ADP
ma-51	35	20	(	(	PUNCT
ma-51	35	21	1.3	1.3	NUM
ma-51	35	22	)	)	PUNCT
ma-51	35	23	.	.	PUNCT
ma-51	36	1	the	the	DET
ma-51	36	2	class	class	NOUN
ma-51	36	3	of	of	ADP
ma-51	36	4	pseudocontractive	pseudocontractive	ADJ
ma-51	36	5	maps	map	NOUN
ma-51	36	6	is	be	AUX
ma-51	36	7	a	a	DET
ma-51	36	8	proper	proper	ADJ
ma-51	36	9	subclass	subclass	NOUN
ma-51	36	10	of	of	ADP
ma-51	36	11	the	the	DET
ma-51	36	12	class	class	NOUN
ma-51	36	13	of	of	ADP
ma-51	36	14	hemicontractive	hemicontractive	ADJ
ma-51	36	15	maps	map	NOUN
ma-51	36	16	.	.	PUNCT
ma-51	37	1	again	again	ADV
ma-51	37	2	,	,	PUNCT
ma-51	37	3	the	the	DET
ma-51	37	4	class	class	NOUN
ma-51	37	5	of	of	ADP
ma-51	37	6	demicontractive	demicontractive	ADJ
ma-51	37	7	maps	map	NOUN
ma-51	37	8	is	be	AUX
ma-51	37	9	a	a	DET
ma-51	37	10	proper	proper	ADJ
ma-51	37	11	subclass	subclass	NOUN
ma-51	37	12	of	of	ADP
ma-51	37	13	the	the	DET
ma-51	37	14	class	class	NOUN
ma-51	37	15	of	of	ADP
ma-51	37	16	hemicontractive	hemicontractive	ADJ
ma-51	37	17	maps	map	NOUN
ma-51	37	18	(	(	PUNCT
ma-51	37	19	see	see	VERB
ma-51	37	20	,	,	PUNCT
ma-51	37	21	for	for	ADP
ma-51	37	22	example	example	NOUN
ma-51	37	23	,	,	PUNCT
ma-51	37	24	[	[	X
ma-51	37	25	?	?	X
ma-51	37	26	]	]	X
ma-51	37	27	)	)	PUNCT
ma-51	37	28	.	.	PUNCT
ma-51	38	1	these	these	DET
ma-51	38	2	two	two	NUM
ma-51	38	3	classes	class	NOUN
ma-51	38	4	of	of	ADP
ma-51	38	5	mappings	mapping	NOUN
ma-51	38	6	have	have	AUX
ma-51	38	7	been	be	AUX
ma-51	38	8	studied	study	VERB
ma-51	38	9	extensively	extensively	ADV
ma-51	38	10	by	by	ADP
ma-51	38	11	many	many	ADJ
ma-51	38	12	researchers	researcher	NOUN
ma-51	38	13	(	(	PUNCT
ma-51	38	14	see	see	VERB
ma-51	38	15	,	,	PUNCT
ma-51	38	16	for	for	ADP
ma-51	38	17	example	example	NOUN
ma-51	38	18	,	,	PUNCT
ma-51	38	19	[	[	X
ma-51	38	20	?	?	X
ma-51	38	21	]	]	X
ma-51	38	22	,	,	PUNCT
ma-51	38	23	[	[	X
ma-51	38	24	13	13	NUM
ma-51	38	25	]	]	PUNCT
ma-51	38	26	,	,	PUNCT
ma-51	38	27	[	[	X
ma-51	38	28	17	17	NUM
ma-51	38	29	]	]	PUNCT
ma-51	38	30	and	and	CCONJ
ma-51	38	31	the	the	DET
ma-51	38	32	references	reference	NOUN
ma-51	38	33	therein	therein	ADV
ma-51	38	34	)	)	PUNCT
ma-51	38	35	.	.	PUNCT
ma-51	39	1	v.	v.	ADP
ma-51	39	2	t	t	PROPN
ma-51	39	3	is	be	AUX
ma-51	39	4	called	call	VERB
ma-51	39	5	α	α	NOUN
ma-51	39	6	-	-	PUNCT
ma-51	39	7	demicontraction	demicontraction	NOUN
ma-51	39	8	(	(	PUNCT
ma-51	39	9	see	see	VERB
ma-51	39	10	,	,	PUNCT
ma-51	39	11	for	for	ADP
ma-51	39	12	examole	examole	NOUN
ma-51	39	13	,	,	PUNCT
ma-51	39	14	[	[	X
ma-51	39	15	13	13	NUM
ma-51	39	16	]	]	PUNCT
ma-51	39	17	)	)	PUNCT
ma-51	40	1	if	if	SCONJ
ma-51	40	2	f	f	PROPN
ma-51	40	3	(	(	PUNCT
ma-51	40	4	t	t	PROPN
ma-51	40	5	)	)	PUNCT
ma-51	40	6	=	=	PRON
ma-51	40	7	{	{	PUNCT
ma-51	40	8	x	x	PUNCT
ma-51	40	9	∈	∈	PROPN
ma-51	40	10	k	k	NOUN
ma-51	40	11	:	:	PUNCT
ma-51	40	12	x	x	X
ma-51	40	13	=	=	SYM
ma-51	40	14	tx	tx	PROPN
ma-51	40	15	}	}	PUNCT
ma-51	40	16	6=	6=	ADP
ma-51	40	17	∅	∅	NOUN
ma-51	40	18	and	and	CCONJ
ma-51	40	19	∀(s	∀(s	NUM
ma-51	40	20	×	×	PROPN
ma-51	40	21	q	q	NOUN
ma-51	40	22	)	)	PUNCT
ma-51	40	23	∈	∈	PROPN
ma-51	40	24	(	(	PUNCT
ma-51	40	25	k	k	PROPN
ma-51	40	26	×	×	PROPN
ma-51	40	27	f	f	X
ma-51	40	28	(	(	PUNCT
ma-51	40	29	t	t	PROPN
ma-51	40	30	)	)	PUNCT
ma-51	40	31	)	)	PUNCT
ma-51	40	32	,	,	PUNCT
ma-51	40	33	there	there	PRON
ma-51	40	34	exist	exist	VERB
ma-51	40	35	λ	λ	PROPN
ma-51	40	36	>	>	X
ma-51	40	37	0	0	PUNCT
ma-51	41	1	and	and	CCONJ
ma-51	41	2	α	α	PRON
ma-51	41	3	≥	≥	NUM
ma-51	41	4	1	1	NUM
ma-51	41	5	such	such	ADJ
ma-51	41	6	that	that	SCONJ
ma-51	41	7	the	the	DET
ma-51	41	8	inequality	inequality	NOUN
ma-51	41	9	〈	〈	PROPN
ma-51	41	10	s	s	PART
ma-51	41	11	−	−	NOUN
ma-51	41	12	ts	ts	NOUN
ma-51	41	13	,	,	PUNCT
ma-51	41	14	s	s	VERB
ma-51	41	15	−	−	PROPN
ma-51	41	16	αq	αq	ADP
ma-51	41	17	〉	〉	PROPN
ma-51	41	18	≥	≥	NOUN
ma-51	41	19	λ‖s	λ‖s	PROPN
ma-51	41	20	−	−	PROPN
ma-51	41	21	ts‖2,∀(s	ts‖2,∀(s	NOUN
ma-51	41	22	×	×	PROPN
ma-51	41	23	q	q	NOUN
ma-51	41	24	)	)	PUNCT
ma-51	41	25	∈	∈	PROPN
ma-51	41	26	(	(	PUNCT
ma-51	41	27	k	k	PROPN
ma-51	41	28	×	×	PROPN
ma-51	41	29	f	f	X
ma-51	41	30	(	(	PUNCT
ma-51	41	31	t	t	PROPN
ma-51	41	32	)	)	PUNCT
ma-51	41	33	)	)	PUNCT
ma-51	41	34	.	.	PUNCT
ma-51	42	1	(	(	PUNCT
ma-51	42	2	1.5	1.5	NUM
ma-51	42	3	)	)	PUNCT
ma-51	42	4	holds	hold	VERB
ma-51	42	5	.	.	PUNCT
ma-51	43	1	clearly	clearly	ADV
ma-51	43	2	,	,	PUNCT
ma-51	43	3	(	(	PUNCT
ma-51	43	4	1.5	1.5	NUM
ma-51	43	5	)	)	PUNCT
ma-51	43	6	is	be	AUX
ma-51	43	7	equivalent	equivalent	ADJ
ma-51	43	8	to	to	ADP
ma-51	43	9	‖ts	‖ts	NUM
ma-51	43	10	−	−	NOUN
ma-51	43	11	αq‖2	αq‖2	PROPN
ma-51	43	12	≤	≤	NUM
ma-51	43	13	‖s	‖s	ADV
ma-51	43	14	−	−	PROPN
ma-51	44	1	αq‖2	αq‖2	NOUN
ma-51	44	2	+	+	CCONJ
ma-51	44	3	k‖s	k‖	NOUN
ma-51	44	4	−	−	PROPN
ma-51	44	5	ts‖2	ts‖2	PROPN
ma-51	44	6	,	,	PUNCT
ma-51	44	7	(	(	PUNCT
ma-51	44	8	1.6	1.6	NUM
ma-51	44	9	)	)	PUNCT
ma-51	44	10	where	where	SCONJ
ma-51	44	11	k	k	PROPN
ma-51	44	12	=	=	SYM
ma-51	44	13	1−	1−	NUM
ma-51	44	14	2λ	2λ	NUM
ma-51	44	15	∈	∈	PROPN
ma-51	45	1	[	[	X
ma-51	45	2	0	0	NUM
ma-51	45	3	,	,	PUNCT
ma-51	45	4	1	1	NUM
ma-51	45	5	)	)	PUNCT
ma-51	45	6	.	.	PUNCT
ma-51	46	1	v.	v.	ADP
ma-51	46	2	t	t	PROPN
ma-51	46	3	is	be	AUX
ma-51	46	4	called	call	VERB
ma-51	46	5	α	α	PRON
ma-51	46	6	-	-	NOUN
ma-51	46	7	hemicontraction	hemicontraction	NOUN
ma-51	46	8	(	(	PUNCT
ma-51	46	9	see	see	VERB
ma-51	46	10	,	,	PUNCT
ma-51	46	11	for	for	ADP
ma-51	46	12	examole	examole	NOUN
ma-51	46	13	,	,	PUNCT
ma-51	46	14	[	[	X
ma-51	46	15	17	17	NUM
ma-51	46	16	]	]	PUNCT
ma-51	46	17	)	)	PUNCT
ma-51	46	18	if	if	SCONJ
ma-51	46	19	f	f	PROPN
ma-51	46	20	(	(	PUNCT
ma-51	46	21	t	t	PROPN
ma-51	46	22	)	)	PUNCT
ma-51	47	1	=	=	PRON
ma-51	48	1	{	{	PUNCT
ma-51	48	2	x	x	PUNCT
ma-51	48	3	∈	∈	PROPN
ma-51	48	4	k	k	NOUN
ma-51	48	5	:	:	PUNCT
ma-51	48	6	x	x	X
ma-51	48	7	=	=	SYM
ma-51	48	8	tx	tx	PROPN
ma-51	48	9	}	}	PUNCT
ma-51	48	10	6=	6=	ADP
ma-51	48	11	∅	∅	NOUN
ma-51	48	12	and	and	CCONJ
ma-51	48	13	∀(s	∀(s	NUM
ma-51	48	14	×	×	PROPN
ma-51	48	15	q	q	NOUN
ma-51	48	16	)	)	PUNCT
ma-51	48	17	∈	∈	PROPN
ma-51	48	18	(	(	PUNCT
ma-51	48	19	k	k	PROPN
ma-51	48	20	×	×	PROPN
ma-51	48	21	f	f	X
ma-51	48	22	(	(	PUNCT
ma-51	48	23	t	t	PROPN
ma-51	48	24	)	)	PUNCT
ma-51	48	25	)	)	PUNCT
ma-51	48	26	,	,	PUNCT
ma-51	48	27	there	there	PRON
ma-51	48	28	exists	exist	VERB
ma-51	48	29	α	α	PRON
ma-51	48	30	≥	≥	NUM
ma-51	48	31	1	1	NUM
ma-51	48	32	such	such	ADJ
ma-51	48	33	that	that	SCONJ
ma-51	48	34	the	the	DET
ma-51	48	35	inequality	inequality	NOUN
ma-51	48	36	‖ts	‖ts	NUM
ma-51	48	37	−	−	NOUN
ma-51	48	38	αq‖2	αq‖2	PROPN
ma-51	48	39	≤	≤	NUM
ma-51	48	40	‖s	‖s	ADV
ma-51	48	41	−	−	PROPN
ma-51	48	42	αq‖2	αq‖2	PROPN
ma-51	48	43	+	+	CCONJ
ma-51	48	44	‖s	‖s	ADJ
ma-51	48	45	−	−	PROPN
ma-51	48	46	ts‖2	ts‖2	PROPN
ma-51	48	47	(	(	PUNCT
ma-51	48	48	1.7	1.7	NUM
ma-51	48	49	)	)	PUNCT
ma-51	48	50	holds	hold	VERB
ma-51	48	51	.	.	PUNCT
ma-51	49	1	observe	observe	VERB
ma-51	49	2	that	that	SCONJ
ma-51	49	3	(	(	PUNCT
ma-51	49	4	1.7	1.7	NUM
ma-51	49	5	)	)	PUNCT
ma-51	49	6	is	be	AUX
ma-51	49	7	equivalent	equivalent	ADJ
ma-51	49	8	to	to	ADP
ma-51	49	9	〈	〈	PROPN
ma-51	49	10	s	s	PART
ma-51	49	11	−	−	NOUN
ma-51	49	12	ts	ts	NOUN
ma-51	49	13	,	,	PUNCT
ma-51	49	14	s	s	VERB
ma-51	49	15	−	−	PROPN
ma-51	49	16	αq	αq	PROPN
ma-51	49	17	〉	〉	PROPN
ma-51	49	18	≥	≥	NOUN
ma-51	49	19	0,∀(s	0,∀(s	NUM
ma-51	49	20	×	×	PROPN
ma-51	49	21	q	q	NOUN
ma-51	49	22	)	)	PUNCT
ma-51	49	23	∈	∈	PROPN
ma-51	49	24	(	(	PUNCT
ma-51	49	25	k	k	PROPN
ma-51	49	26	×	×	PROPN
ma-51	49	27	f	f	X
ma-51	49	28	(	(	PUNCT
ma-51	49	29	t	t	PROPN
ma-51	49	30	)	)	PUNCT
ma-51	49	31	)	)	PUNCT
ma-51	49	32	.	.	PUNCT
ma-51	50	1	(	(	PUNCT
ma-51	50	2	1.8	1.8	NUM
ma-51	50	3	)	)	PUNCT
ma-51	50	4	in	in	ADP
ma-51	50	5	[	[	PUNCT
ma-51	50	6	[	[	X
ma-51	50	7	17	17	NUM
ma-51	50	8	]	]	PUNCT
ma-51	50	9	,	,	PUNCT
ma-51	50	10	example	example	NOUN
ma-51	50	11	2.2	2.2	NUM
ma-51	50	12	]	]	PUNCT
ma-51	50	13	,	,	PUNCT
ma-51	50	14	osilike	osilike	ADP
ma-51	50	15	and	and	CCONJ
ma-51	50	16	onah	onah	PROPN
ma-51	50	17	gave	give	VERB
ma-51	50	18	an	an	DET
ma-51	50	19	example	example	NOUN
ma-51	50	20	of	of	ADP
ma-51	50	21	α	α	NOUN
ma-51	50	22	-	-	ADJ
ma-51	50	23	hemicontractive	hemicontractive	ADJ
ma-51	50	24	mapping	mapping	NOUN
ma-51	50	25	with	with	ADP
ma-51	50	26	α	α	PROPN
ma-51	50	27	>	>	X
ma-51	50	28	1	1	NUM
ma-51	50	29	which	which	PRON
ma-51	50	30	is	be	AUX
ma-51	50	31	not	not	PART
ma-51	50	32	hemicontractive	hemicontractive	ADJ
ma-51	50	33	mapping	mapping	NOUN
ma-51	50	34	,	,	PUNCT
ma-51	50	35	and	and	CCONJ
ma-51	50	36	also	also	ADV
ma-51	50	37	showed	show	VERB
ma-51	50	38	that	that	SCONJ
ma-51	50	39	there	there	PRON
ma-51	50	40	are	be	VERB
ma-51	50	41	hemicontractive	hemicontractive	ADJ
ma-51	50	42	(	(	PUNCT
ma-51	50	43	1	1	NUM
ma-51	50	44	-	-	PUNCT
ma-51	50	45	hemicontractive	hemicontractive	ADJ
ma-51	50	46	)	)	PUNCT
ma-51	50	47	mappings	mapping	NOUN
ma-51	50	48	which	which	PRON
ma-51	50	49	are	be	AUX
ma-51	50	50	not	not	PART
ma-51	50	51	α	α	NOUN
ma-51	50	52	-	-	NOUN
ma-51	50	53	hemicontraction	hemicontraction	NOUN
ma-51	50	54	for	for	ADP
ma-51	50	55	α	α	PROPN
ma-51	50	56	>	>	X
ma-51	50	57	1(see	1(see	PROPN
ma-51	51	1	[	[	PUNCT
ma-51	51	2	[	[	X
ma-51	51	3	17	17	NUM
ma-51	51	4	]	]	PUNCT
ma-51	51	5	,	,	PUNCT
ma-51	51	6	example	example	NOUN
ma-51	51	7	2.1	2.1	NUM
ma-51	51	8	]	]	PUNCT
ma-51	51	9	for	for	ADP
ma-51	51	10	details	detail	NOUN
ma-51	51	11	)	)	PUNCT
ma-51	51	12	.	.	PUNCT
ma-51	52	1	again	again	ADV
ma-51	52	2	,	,	PUNCT
ma-51	52	3	osilike	osilike	ADP
ma-51	52	4	and	and	CCONJ
ma-51	52	5	onah	onah	PROPN
ma-51	53	1	[	[	X
ma-51	53	2	17	17	NUM
ma-51	53	3	]	]	PUNCT
ma-51	53	4	presented	present	VERB
ma-51	53	5	an	an	DET
ma-51	53	6	example	example	NOUN
ma-51	53	7	of	of	ADP
ma-51	53	8	a	a	DET
ma-51	53	9	mapping	mapping	NOUN
ma-51	53	10	which	which	PRON
ma-51	53	11	is	be	AUX
ma-51	53	12	hemicontractive	hemicontractive	ADJ
ma-51	53	13	(	(	PUNCT
ma-51	53	14	1	1	NUM
ma-51	53	15	-	-	NUM
ma-51	53	16	hemicontractive	hemicontractive	NOUN
ma-51	53	17	)	)	PUNCT
ma-51	53	18	and	and	CCONJ
ma-51	53	19	alpha	alpha	NOUN
ma-51	53	20	-	-	PUNCT
ma-51	53	21	hemicontractive	hemicontractive	ADJ
ma-51	53	22	mapping	mapping	NOUN
ma-51	53	23	for	for	ADP
ma-51	53	24	α	α	PROPN
ma-51	53	25	>	>	X
ma-51	53	26	1	1	NUM
ma-51	53	27	but	but	CCONJ
ma-51	53	28	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	53	29	eur	eur	PROPN
ma-51	53	30	.	.	PUNCT
ma-51	54	1	j.	j.	PROPN
ma-51	54	2	math	math	PROPN
ma-51	54	3	.	.	PUNCT
ma-51	55	1	anal	anal	PROPN
ma-51	55	2	.	.	PUNCT
ma-51	56	1	10.28924	10.28924	NUM
ma-51	56	2	/	/	SYM
ma-51	56	3	ada	ada	PROPN
ma-51	56	4	/	/	SYM
ma-51	56	5	ma.2.10	ma.2.10	PROPN
ma-51	56	6	3	3	NUM
ma-51	56	7	neither	neither	CCONJ
ma-51	56	8	demicontractive	demicontractive	ADJ
ma-51	56	9	(	(	PUNCT
ma-51	56	10	1	1	NUM
ma-51	56	11	-	-	PUNCT
ma-51	56	12	demicontractive	demicontractive	NOUN
ma-51	56	13	)	)	PUNCT
ma-51	56	14	nor	nor	CCONJ
ma-51	56	15	α	α	X
ma-51	56	16	-	-	PUNCT
ma-51	56	17	demicontractive	demicontractive	ADJ
ma-51	56	18	mapping	mapping	NOUN
ma-51	56	19	for	for	ADP
ma-51	56	20	α	α	PROPN
ma-51	56	21	>	>	X
ma-51	56	22	1(see	1(see	PROPN
ma-51	57	1	[	[	X
ma-51	57	2	17	17	NUM
ma-51	57	3	]	]	PUNCT
ma-51	57	4	,	,	PUNCT
ma-51	57	5	example	example	NOUN
ma-51	57	6	2.3	2.3	NUM
ma-51	57	7	for	for	ADP
ma-51	57	8	details	detail	NOUN
ma-51	57	9	)	)	PUNCT
ma-51	57	10	.	.	PUNCT
ma-51	58	1	for	for	ADP
ma-51	58	2	further	further	ADJ
ma-51	58	3	cheracterisation	cheracterisation	NOUN
ma-51	58	4	of	of	ADP
ma-51	58	5	α	α	NOUN
ma-51	58	6	-	-	ADJ
ma-51	58	7	hemicontractive	hemicontractive	ADJ
ma-51	58	8	mapping	mapping	NOUN
ma-51	58	9	,	,	PUNCT
ma-51	58	10	interested	interested	ADJ
ma-51	58	11	reader	reader	NOUN
ma-51	58	12	should	should	AUX
ma-51	58	13	consult	consult	VERB
ma-51	58	14	[	[	X
ma-51	58	15	17	17	NUM
ma-51	58	16	]	]	PUNCT
ma-51	58	17	.	.	PUNCT
ma-51	59	1	a	a	DET
ma-51	59	2	mapping	mapping	NOUN
ma-51	59	3	t	t	NOUN
ma-51	59	4	:	:	PUNCT
ma-51	59	5	h	h	NOUN
ma-51	59	6	−→	−→	ADJ
ma-51	59	7	h	h	NOUN
ma-51	59	8	is	be	AUX
ma-51	59	9	called	call	VERB
ma-51	59	10	ν	ν	ADV
ma-51	59	11	-	-	PUNCT
ma-51	59	12	strongly	strongly	ADV
ma-51	59	13	monotone	monotone	ADJ
ma-51	59	14	if	if	SCONJ
ma-51	59	15	there	there	PRON
ma-51	59	16	exists	exist	VERB
ma-51	59	17	ν	ν	X
ma-51	59	18	>	>	X
ma-51	59	19	0	0	NUM
ma-51	59	20	such	such	ADJ
ma-51	59	21	that	that	SCONJ
ma-51	59	22	〈	〈	PROPN
ma-51	59	23	s	s	PART
ma-51	59	24	−	−	NOUN
ma-51	59	25	ts	ts	NOUN
ma-51	59	26	,	,	PUNCT
ma-51	59	27	s	s	PART
ma-51	59	28	−	−	PROPN
ma-51	59	29	z	z	PROPN
ma-51	59	30	〉	〉	PROPN
ma-51	59	31	≥	≥	NOUN
ma-51	59	32	ν‖s	ν‖s	PROPN
ma-51	59	33	−	−	PROPN
ma-51	59	34	z‖2,∀s	z‖2,∀s	NUM
ma-51	59	35	,	,	PUNCT
ma-51	59	36	z	z	PROPN
ma-51	59	37	∈	∈	PROPN
ma-51	59	38	h	h	PROPN
ma-51	59	39	..	..	PUNCT
ma-51	59	40	(	(	PUNCT
ma-51	59	41	1.9	1.9	NUM
ma-51	59	42	)	)	PUNCT
ma-51	59	43	iterative	iterative	NOUN
ma-51	59	44	method	method	NOUN
ma-51	59	45	for	for	ADP
ma-51	59	46	approximating	approximate	VERB
ma-51	59	47	fixed	fix	VERB
ma-51	59	48	point	point	NOUN
ma-51	59	49	of	of	ADP
ma-51	59	50	l	l	ADJ
ma-51	59	51	-	-	ADJ
ma-51	59	52	lipschitz	lipschitz	ADJ
ma-51	59	53	pseudocontractive	pseudocontractive	ADJ
ma-51	59	54	mapping	mapping	NOUN
ma-51	59	55	has	have	VERB
ma-51	59	56	beenan	beenan	NOUN
ma-51	59	57	active	active	ADJ
ma-51	59	58	area	area	NOUN
ma-51	59	59	of	of	ADP
ma-51	59	60	investigation	investigation	NOUN
ma-51	59	61	in	in	ADP
ma-51	59	62	recent	recent	ADJ
ma-51	59	63	times	time	NOUN
ma-51	59	64	(	(	PUNCT
ma-51	59	65	see	see	VERB
ma-51	59	66	,	,	PUNCT
ma-51	59	67	for	for	ADP
ma-51	59	68	example	example	NOUN
ma-51	59	69	,	,	PUNCT
ma-51	60	1	[	[	X
ma-51	60	2	?	?	X
ma-51	60	3	]	]	X
ma-51	60	4	,	,	PUNCT
ma-51	60	5	[	[	X
ma-51	60	6	?	?	X
ma-51	60	7	]	]	X
ma-51	60	8	,	,	PUNCT
ma-51	60	9	[	[	X
ma-51	60	10	20	20	NUM
ma-51	60	11	]	]	PUNCT
ma-51	60	12	,	,	PUNCT
ma-51	60	13	[	[	X
ma-51	60	14	14	14	NUM
ma-51	60	15	]	]	PUNCT
ma-51	60	16	,	,	PUNCT
ma-51	60	17	[	[	X
ma-51	60	18	26	26	NUM
ma-51	60	19	]	]	PUNCT
ma-51	60	20	,	,	PUNCT
ma-51	60	21	[	[	X
ma-51	60	22	27	27	NUM
ma-51	60	23	]	]	PUNCT
ma-51	60	24	and	and	CCONJ
ma-51	60	25	thereferences	thereference	NOUN
ma-51	60	26	contained	contain	VERB
ma-51	60	27	in	in	ADP
ma-51	60	28	them	they	PRON
ma-51	60	29	)	)	PUNCT
ma-51	60	30	.	.	PUNCT
ma-51	61	1	in	in	ADP
ma-51	61	2	[	[	X
ma-51	61	3	24	24	NUM
ma-51	61	4	]	]	PUNCT
ma-51	61	5	,	,	PUNCT
ma-51	61	6	voluhan	voluhan	PROPN
ma-51	61	7	introduced	introduce	VERB
ma-51	61	8	the	the	DET
ma-51	61	9	modified	modify	VERB
ma-51	61	10	projection	projection	NOUN
ma-51	61	11	-	-	PUNCT
ma-51	61	12	type	type	NOUN
ma-51	61	13	ishikawaiterative	ishikawaiterative	NOUN
ma-51	61	14	method	method	NOUN
ma-51	61	15	in	in	ADP
ma-51	61	16	the	the	DET
ma-51	61	17	following	following	ADJ
ma-51	61	18	way	way	NOUN
ma-51	61	19	:	:	PUNCT
ma-51	61	20	let	let	VERB
ma-51	61	21	h	h	NOUN
ma-51	61	22	be	be	AUX
ma-51	61	23	a	a	DET
ma-51	61	24	hilbert	hilbert	NOUN
ma-51	61	25	space	space	NOUN
ma-51	61	26	,	,	PUNCT
ma-51	61	27	k	k	PROPN
ma-51	61	28	nonempty	nonempty	X
ma-51	61	29	,	,	PUNCT
ma-51	61	30	closed	closed	ADJ
ma-51	61	31	and	and	CCONJ
ma-51	61	32	convexsubset	convexsubset	NOUN
ma-51	61	33	of	of	ADP
ma-51	61	34	h	h	NOUN
ma-51	61	35	and	and	CCONJ
ma-51	61	36	t	t	PROPN
ma-51	61	37	:	:	PUNCT
ma-51	62	1	k	k	X
ma-51	62	2	−→	−→	NOUN
ma-51	62	3	k	k	PROPN
ma-51	62	4	be	be	AUX
ma-51	62	5	an	an	DET
ma-51	62	6	l	l	NOUN
ma-51	62	7	-	-	PUNCT
ma-51	62	8	lipshitz	lipshitz	NOUN
ma-51	62	9	pseudocontractive	pseudocontractive	ADJ
ma-51	62	10	mapping	mapping	NOUN
ma-51	62	11	.	.	PUNCT
ma-51	63	1	for	for	ADP
ma-51	63	2	an	an	DET
ma-51	63	3	arbitrary	arbitrary	ADJ
ma-51	63	4	x0	x0	PROPN
ma-51	63	5	∈	∈	PROPN
ma-51	63	6	k	k	NOUN
ma-51	63	7	,	,	PUNCT
ma-51	63	8	define	define	VERB
ma-51	63	9	the	the	DET
ma-51	63	10	sequence	sequence	NOUN
ma-51	63	11	{	{	PUNCT
ma-51	63	12	xn}∞n=0	xn}∞n=0	X
ma-51	63	13	iteratively	iteratively	ADV
ma-51	63	14	as	as	SCONJ
ma-51	63	15	follows.	follows.	NOUN
ma-51	63	16	xn+1	xn+1	PROPN
ma-51	63	17	=	=	SYM
ma-51	63	18	pk	pk	X
ma-51	63	19	[	[	X
ma-51	63	20	(	(	PUNCT
ma-51	63	21	1−	1−	NUM
ma-51	63	22	αn	αn	NOUN
ma-51	63	23	−	−	PROPN
ma-51	63	24	γn)xn	γn)xn	PROPN
ma-51	63	25	+	+	CCONJ
ma-51	63	26	γntyn	γntyn	PROPN
ma-51	64	1	]	]	X
ma-51	64	2	yn	yn	PROPN
ma-51	64	3	=	=	SYM
ma-51	64	4	(	(	PUNCT
ma-51	64	5	1−	1−	NUM
ma-51	64	6	βn)xn	βn)xn	PROPN
ma-51	64	7	+	+	CCONJ
ma-51	64	8	βntxn	βntxn	ADJ
ma-51	64	9	,	,	PUNCT
ma-51	64	10	n	n	PRON
ma-51	64	11	≥	≥	NOUN
ma-51	64	12	1	1	NUM
ma-51	64	13	,	,	PUNCT
ma-51	64	14	(	(	PUNCT
ma-51	64	15	1.10	1.10	NUM
ma-51	64	16	)	)	PUNCT
ma-51	64	17	where	where	SCONJ
ma-51	64	18	{	{	PUNCT
ma-51	64	19	αn}∞n=0	αn}∞n=0	NUM
ma-51	64	20	,	,	PUNCT
ma-51	64	21	{	{	PUNCT
ma-51	64	22	βn}∞n=0	βn}∞n=0	X
ma-51	64	23	,	,	PUNCT
ma-51	64	24	{	{	PUNCT
ma-51	64	25	γn}∞n=0	γn}∞n=0	NUM
ma-51	64	26	∈	∈	PROPN
ma-51	64	27	(	(	PUNCT
ma-51	64	28	0	0	NUM
ma-51	64	29	,	,	PUNCT
ma-51	64	30	1	1	NUM
ma-51	64	31	)	)	PUNCT
ma-51	64	32	and	and	CCONJ
ma-51	64	33	pk	pk	NOUN
ma-51	64	34	is	be	AUX
ma-51	64	35	a	a	DET
ma-51	64	36	projection	projection	NOUN
ma-51	64	37	map	map	NOUN
ma-51	64	38	from	from	ADP
ma-51	64	39	h	h	NOUN
ma-51	64	40	onto	onto	ADP
ma-51	64	41	k.	k.	PROPN
ma-51	64	42	using(1.10	using(1.10	PROPN
ma-51	64	43	)	)	PUNCT
ma-51	64	44	,	,	PUNCT
ma-51	64	45	she	she	PRON
ma-51	64	46	proved	prove	VERB
ma-51	64	47	the	the	DET
ma-51	64	48	following	follow	VERB
ma-51	64	49	theorem	theorem	ADJ
ma-51	64	50	.	.	PUNCT
ma-51	64	51	theorem	theorem	VERB
ma-51	64	52	1.1	1.1	NUM
ma-51	64	53	.	.	PUNCT
ma-51	65	1	let	let	VERB
ma-51	65	2	h	h	PRON
ma-51	65	3	be	be	AUX
ma-51	65	4	a	a	DET
ma-51	65	5	hilbert	hilbert	NOUN
ma-51	65	6	space	space	NOUN
ma-51	65	7	,	,	PUNCT
ma-51	65	8	d	d	X
ma-51	65	9	a	a	DET
ma-51	65	10	nonempty	nonempty	ADV
ma-51	65	11	closed	close	VERB
ma-51	65	12	convex	convex	NOUN
ma-51	65	13	subset	subset	NOUN
ma-51	65	14	of	of	ADP
ma-51	65	15	h	h	PROPN
ma-51	65	16	and	and	CCONJ
ma-51	65	17	t	t	PROPN
ma-51	65	18	:	:	PUNCT
ma-51	66	1	d	d	X
ma-51	66	2	−→	−→	NOUN
ma-51	66	3	d	d	X
ma-51	66	4	an	an	DET
ma-51	66	5	l	l	ADJ
ma-51	66	6	-	-	ADJ
ma-51	66	7	lipschitz	lipschitz	ADJ
ma-51	66	8	pseudocontractive	pseudocontractive	ADJ
ma-51	66	9	mapping	mapping	NOUN
ma-51	66	10	such	such	ADJ
ma-51	66	11	that	that	SCONJ
ma-51	66	12	f	f	PROPN
ma-51	66	13	(	(	PUNCT
ma-51	66	14	t	t	PROPN
ma-51	66	15	)	)	PUNCT
ma-51	66	16	6=	6=	ADP
ma-51	66	17	∅.	∅.	VERB
ma-51	66	18	for	for	ADP
ma-51	66	19	any	any	DET
ma-51	66	20	given	give	VERB
ma-51	66	21	x0	x0	PROPN
ma-51	66	22	∈	∈	PROPN
ma-51	66	23	h	h	NOUN
ma-51	66	24	,	,	PUNCT
ma-51	66	25	let	let	VERB
ma-51	66	26	{	{	PUNCT
ma-51	66	27	xn}∞n=0	xn}∞n=0	X
ma-51	66	28	be	be	AUX
ma-51	66	29	the	the	DET
ma-51	66	30	sequence	sequence	NOUN
ma-51	66	31	defined	define	VERB
ma-51	66	32	by	by	ADP
ma-51	66	33	(	(	PUNCT
ma-51	66	34	1.10	1.10	NUM
ma-51	66	35	)	)	PUNCT
ma-51	66	36	.	.	PUNCT
ma-51	67	1	assume	assume	VERB
ma-51	67	2	the	the	DET
ma-51	67	3	sequences	sequence	NOUN
ma-51	67	4	{	{	PUNCT
ma-51	67	5	αn}∞n=0	αn}∞n=0	NUM
ma-51	67	6	,	,	PUNCT
ma-51	67	7	{	{	PUNCT
ma-51	67	8	βn}∞n=0	βn}∞n=0	X
ma-51	67	9	,	,	PUNCT
ma-51	67	10	{	{	PUNCT
ma-51	67	11	γn}∞n=0	γn}∞n=0	NUM
ma-51	67	12	∈	∈	PROPN
ma-51	67	13	(	(	PUNCT
ma-51	67	14	0	0	NUM
ma-51	67	15	,	,	PUNCT
ma-51	67	16	1	1	NUM
ma-51	67	17	)	)	PUNCT
ma-51	67	18	satisfy(1	satisfy(1	PROPN
ma-51	67	19	)	)	PUNCT
ma-51	68	1	βn(1−	βn(1−	ADJ
ma-51	68	2	αn	αn	NOUN
ma-51	68	3	)	)	PUNCT
ma-51	68	4	>	>	X
ma-51	69	1	γn,∀n	γn,∀n	PROPN
ma-51	69	2	≥	≥	NUM
ma-51	69	3	1;(2	1;(2	NUM
ma-51	69	4	)	)	PUNCT
ma-51	69	5	limn→∞	limn→∞	PROPN
ma-51	69	6	αn	αn	NOUN
ma-51	70	1	=	=	SYM
ma-51	70	2	0	0	NUM
ma-51	70	3	and	and	CCONJ
ma-51	70	4	∑∞	∑∞	NOUN
ma-51	70	5	n=0	n=0	NUM
ma-51	70	6	αn	αn	NOUN
ma-51	71	1	=	=	SYM
ma-51	71	2	∞;(3	∞;(3	PROPN
ma-51	71	3	)	)	PUNCT
ma-51	71	4	0	0	PUNCT
ma-51	71	5	<	<	X
ma-51	71	6	α	α	PROPN
ma-51	71	7	≤	≤	NOUN
ma-51	71	8	γn	γn	ADP
ma-51	71	9	≤	≤	NUM
ma-51	71	10	βn	βn	VERB
ma-51	71	11	≤	≤	PUNCT
ma-51	71	12	β	β	X
ma-51	71	13	<	<	X
ma-51	71	14	1√	1√	PROPN
ma-51	71	15	1	1	NUM
ma-51	71	16	+	+	NUM
ma-51	71	17	l2	l2	NOUN
ma-51	71	18	+	+	CCONJ
ma-51	71	19	1	1	NUM
ma-51	71	20	,	,	PUNCT
ma-51	71	21	∀n	∀n	NUM
ma-51	71	22	≥	≥	NOUN
ma-51	71	23	1	1	NUM
ma-51	71	24	.	.	PUNCT
ma-51	72	1	then	then	ADV
ma-51	72	2	,	,	PUNCT
ma-51	72	3	the	the	DET
ma-51	72	4	sequence	sequence	NOUN
ma-51	72	5	{	{	PUNCT
ma-51	72	6	xn}∞n=0	xn}∞n=0	X
ma-51	72	7	strongly	strongly	ADV
ma-51	72	8	converges	converge	VERB
ma-51	72	9	to	to	ADP
ma-51	72	10	the	the	DET
ma-51	72	11	fixed	fix	VERB
ma-51	72	12	point	point	NOUN
ma-51	72	13	of	of	ADP
ma-51	72	14	t	t	PROPN
ma-51	72	15	.	.	PUNCT
ma-51	73	1	remark	remark	VERB
ma-51	73	2	1.1	1.1	NUM
ma-51	73	3	.	.	PUNCT
ma-51	74	1	if	if	SCONJ
ma-51	74	2	αn	αn	NOUN
ma-51	74	3	=	=	SYM
ma-51	74	4	0,∀n	0,∀n	PROPN
ma-51	74	5	≥	≥	PROPN
ma-51	74	6	1	1	NUM
ma-51	74	7	,	,	PUNCT
ma-51	74	8	and	and	CCONJ
ma-51	74	9	pk	pk	NOUN
ma-51	74	10	is	be	AUX
ma-51	74	11	an	an	DET
ma-51	74	12	identity	identity	NOUN
ma-51	74	13	,	,	PUNCT
ma-51	74	14	(	(	PUNCT
ma-51	74	15	1.10	1.10	NUM
ma-51	74	16	)	)	PUNCT
ma-51	74	17	reduces	reduce	VERB
ma-51	74	18	to	to	ADP
ma-51	74	19	the	the	DET
ma-51	74	20	well	well	ADV
ma-51	74	21	-	-	PUNCT
ma-51	74	22	known	know	VERB
ma-51	74	23	ishikawa	ishikawa	PROPN
ma-51	74	24	iteration	iteration	NOUN
ma-51	74	25	method	method	NOUN
ma-51	74	26			PUNCT
ma-51	74	27	xn+1	xn+1	PROPN
ma-51	74	28	=	=	SYM
ma-51	74	29	(	(	PUNCT
ma-51	74	30	1−	1−	NUM
ma-51	74	31	γn)xn	γn)xn	NOUN
ma-51	74	32	+	+	CCONJ
ma-51	74	33	γntyn	γntyn	NOUN
ma-51	74	34	yn	yn	X
ma-51	74	35	=	=	PUNCT
ma-51	74	36	(	(	PUNCT
ma-51	74	37	1−	1−	NUM
ma-51	74	38	βn)xn	βn)xn	PROPN
ma-51	75	1	+	+	CCONJ
ma-51	75	2	βntxn	βntxn	ADJ
ma-51	75	3	,	,	PUNCT
ma-51	75	4	n	n	PRON
ma-51	75	5	≥	≥	NOUN
ma-51	75	6	1	1	NUM
ma-51	75	7	,	,	PUNCT
ma-51	75	8	(	(	PUNCT
ma-51	75	9	1.11	1.11	NUM
ma-51	75	10	)	)	PUNCT
ma-51	75	11	which	which	PRON
ma-51	75	12	has	have	AUX
ma-51	75	13	been	be	AUX
ma-51	75	14	used	use	VERB
ma-51	75	15	by	by	ADP
ma-51	75	16	several	several	ADJ
ma-51	75	17	researchers	researcher	NOUN
ma-51	75	18	to	to	PART
ma-51	75	19	approximate	approximate	VERB
ma-51	75	20	the	the	DET
ma-51	75	21	fixed	fix	VERB
ma-51	75	22	points	point	NOUN
ma-51	75	23	of	of	ADP
ma-51	75	24	different	different	ADJ
ma-51	75	25	operators	operator	NOUN
ma-51	75	26	or	or	CCONJ
ma-51	75	27	operator	operator	NOUN
ma-51	75	28	equations	equation	NOUN
ma-51	75	29	in	in	ADP
ma-51	75	30	different	different	ADJ
ma-51	75	31	spaces	space	NOUN
ma-51	75	32	.	.	PUNCT
ma-51	76	1	motivated	motivated	ADJ
ma-51	76	2	and	and	CCONJ
ma-51	76	3	inspired	inspire	VERB
ma-51	76	4	by	by	ADP
ma-51	76	5	the	the	DET
ma-51	76	6	works	work	NOUN
ma-51	76	7	in	in	ADP
ma-51	76	8	[	[	X
ma-51	76	9	17	17	NUM
ma-51	76	10	]	]	PUNCT
ma-51	76	11	,	,	PUNCT
ma-51	76	12	[	[	X
ma-51	76	13	24	24	NUM
ma-51	76	14	]	]	PUNCT
ma-51	76	15	and	and	CCONJ
ma-51	76	16	some	some	DET
ma-51	76	17	ongoing	ongoing	ADJ
ma-51	76	18	research	research	NOUN
ma-51	76	19	in	in	ADP
ma-51	76	20	this	this	DET
ma-51	76	21	direction	direction	NOUN
ma-51	76	22	,	,	PUNCT
ma-51	76	23	itis	itis	NOUN
ma-51	76	24	our	our	PRON
ma-51	76	25	purpose	purpose	NOUN
ma-51	76	26	in	in	ADP
ma-51	76	27	this	this	DET
ma-51	76	28	paper	paper	NOUN
ma-51	76	29	to	to	PART
ma-51	76	30	extend	extend	VERB
ma-51	76	31	the	the	DET
ma-51	76	32	results	result	NOUN
ma-51	76	33	in	in	ADP
ma-51	76	34	[	[	X
ma-51	76	35	24	24	NUM
ma-51	76	36	]	]	PUNCT
ma-51	76	37	and	and	CCONJ
ma-51	76	38	other	other	ADJ
ma-51	76	39	related	relate	VERB
ma-51	76	40	results	result	NOUN
ma-51	76	41	from	from	ADP
ma-51	76	42	lipschitzpseudocontractive	lipschitzpseudocontractive	ADJ
ma-51	76	43	mapping	mapping	NOUN
ma-51	76	44	to	to	ADP
ma-51	76	45	the	the	DET
ma-51	76	46	more	more	ADV
ma-51	76	47	general	general	ADJ
ma-51	76	48	α	α	ADJ
ma-51	76	49	-	-	ADJ
ma-51	76	50	hemicontractive	hemicontractive	ADJ
ma-51	76	51	mapping	mapping	NOUN
ma-51	76	52	.	.	PUNCT
ma-51	77	1	our	our	PRON
ma-51	77	2	results	result	NOUN
ma-51	77	3	is	be	AUX
ma-51	77	4	more	more	ADJ
ma-51	77	5	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	77	6	eur	eur	PROPN
ma-51	77	7	.	.	PUNCT
ma-51	78	1	j.	j.	PROPN
ma-51	78	2	math	math	PROPN
ma-51	78	3	.	.	PUNCT
ma-51	79	1	anal	anal	PROPN
ma-51	79	2	.	.	PUNCT
ma-51	80	1	10.28924	10.28924	NUM
ma-51	80	2	/	/	SYM
ma-51	80	3	ada	ada	PROPN
ma-51	80	4	/	/	SYM
ma-51	80	5	ma.2.10	ma.2.10	PROPN
ma-51	80	6	4general	4general	PROPN
ma-51	80	7	and	and	CCONJ
ma-51	80	8	also	also	ADV
ma-51	80	9	more	more	ADV
ma-51	80	10	applicable	applicable	ADJ
ma-51	80	11	because	because	SCONJ
ma-51	80	12	fewer	few	ADJ
ma-51	80	13	and	and	CCONJ
ma-51	80	14	simpler	simple	ADJ
ma-51	80	15	conditions	condition	NOUN
ma-51	80	16	are	be	AUX
ma-51	80	17	required	require	VERB
ma-51	80	18	to	to	PART
ma-51	80	19	attainconvergence	attainconvergence	VERB
ma-51	80	20	.	.	PUNCT
ma-51	81	1	2	2	X
ma-51	81	2	.	.	X
ma-51	81	3	preliminary	preliminary	ADJ
ma-51	81	4	the	the	DET
ma-51	81	5	following	follow	VERB
ma-51	81	6	definitions	definition	NOUN
ma-51	81	7	and	and	CCONJ
ma-51	81	8	lemmas	lemmas	PROPN
ma-51	81	9	will	will	AUX
ma-51	81	10	be	be	AUX
ma-51	81	11	needed	need	VERB
ma-51	81	12	to	to	PART
ma-51	81	13	prove	prove	VERB
ma-51	81	14	our	our	PRON
ma-51	81	15	main	main	ADJ
ma-51	81	16	results	result	NOUN
ma-51	81	17	.	.	PUNCT
ma-51	82	1	definition	definition	NOUN
ma-51	82	2	2.1	2.1	NUM
ma-51	82	3	.	.	PUNCT
ma-51	83	1	(	(	PUNCT
ma-51	83	2	see	see	VERB
ma-51	83	3	[	[	X
ma-51	83	4	27	27	NUM
ma-51	83	5	]	]	PUNCT
ma-51	83	6	)	)	PUNCT
ma-51	83	7	let	let	VERB
ma-51	83	8	h	h	NOUN
ma-51	83	9	and	and	CCONJ
ma-51	83	10	k	k	PROPN
ma-51	83	11	be	be	AUX
ma-51	83	12	as	as	ADV
ma-51	83	13	defined	define	VERB
ma-51	83	14	above	above	ADP
ma-51	83	15	.	.	PUNCT
ma-51	84	1	for	for	ADP
ma-51	84	2	each	each	DET
ma-51	84	3	x	x	SYM
ma-51	84	4	∈	∈	PROPN
ma-51	84	5	h	h	NOUN
ma-51	84	6	,	,	PUNCT
ma-51	84	7	there	there	PRON
ma-51	84	8	exists	exist	VERB
ma-51	84	9	a	a	DET
ma-51	84	10	unique	unique	ADJ
ma-51	84	11	nearest	near	ADJ
ma-51	84	12	point	point	NOUN
ma-51	84	13	of	of	ADP
ma-51	84	14	k	k	NOUN
ma-51	84	15	,	,	PUNCT
ma-51	84	16	denoted	denote	VERB
ma-51	84	17	by	by	ADP
ma-51	84	18	pkx	pkx	PROPN
ma-51	84	19	,	,	PUNCT
ma-51	84	20	such	such	ADJ
ma-51	84	21	that	that	SCONJ
ma-51	84	22	‖x	‖x	PROPN
ma-51	84	23	−	−	PROPN
ma-51	84	24	pkx‖	pkx‖	VERB
ma-51	84	25	≤	≤	NUM
ma-51	84	26	‖x	‖x	PUNCT
ma-51	85	1	−	−	PROPN
ma-51	85	2	y‖,∀y	y‖,∀y	PRON
ma-51	85	3	∈	∈	PROPN
ma-51	85	4	k.	k.	NOUN
ma-51	86	1	such	such	DET
ma-51	86	2	a	a	DET
ma-51	86	3	pk	pk	NOUN
ma-51	86	4	is	be	AUX
ma-51	86	5	called	call	VERB
ma-51	86	6	metric	metric	ADJ
ma-51	86	7	projection	projection	NOUN
ma-51	86	8	from	from	ADP
ma-51	86	9	h	h	PROPN
ma-51	86	10	onto	onto	ADP
ma-51	86	11	k.	k.	NOUN
ma-51	87	1	it	it	PRON
ma-51	87	2	is	be	AUX
ma-51	87	3	well	well	ADV
ma-51	87	4	-	-	PUNCT
ma-51	87	5	known	know	VERB
ma-51	87	6	that	that	SCONJ
ma-51	87	7	pk	pk	NOUN
ma-51	87	8	is	be	AUX
ma-51	87	9	firmly	firmly	ADV
ma-51	87	10	nonexpansive	nonexpansive	ADJ
ma-51	87	11	mapping	mapping	NOUN
ma-51	87	12	from	from	ADP
ma-51	87	13	h	h	PROPN
ma-51	87	14	onto	onto	ADP
ma-51	87	15	k	k	NOUN
ma-51	87	16	;	;	PUNCT
ma-51	87	17	that	that	PRON
ma-51	87	18	is	is	ADV
ma-51	87	19	,	,	PUNCT
ma-51	87	20	‖pkx	‖pkx	PROPN
ma-51	87	21	−	−	PROPN
ma-51	87	22	pky‖2	pky‖2	NOUN
ma-51	87	23	≤	≤	X
ma-51	87	24	〈	〈	AUX
ma-51	87	25	pkx	pkx	VERB
ma-51	87	26	−	−	PROPN
ma-51	87	27	pky	pky	NOUN
ma-51	87	28	,	,	PUNCT
ma-51	87	29	x	x	X
ma-51	87	30	−	−	NOUN
ma-51	88	1	y〉,∀x	y〉,∀x	NOUN
ma-51	88	2	,	,	PUNCT
ma-51	88	3	y	y	PROPN
ma-51	88	4	∈	∈	PROPN
ma-51	88	5	h.	h.	PROPN
ma-51	88	6	also	also	ADV
ma-51	88	7	,	,	PUNCT
ma-51	88	8	for	for	ADP
ma-51	88	9	any	any	DET
ma-51	88	10	x	x	SYM
ma-51	88	11	∈	∈	PROPN
ma-51	88	12	h	h	NOUN
ma-51	88	13	and	and	CCONJ
ma-51	88	14	z	z	NOUN
ma-51	88	15	∈	∈	PROPN
ma-51	89	1	k	k	NOUN
ma-51	89	2	,	,	PUNCT
ma-51	89	3	z	z	NOUN
ma-51	89	4	=	=	SYM
ma-51	89	5	pkx	pkx	VERB
ma-51	89	6	if	if	SCONJ
ma-51	89	7	and	and	CCONJ
ma-51	89	8	only	only	ADV
ma-51	89	9	if	if	SCONJ
ma-51	89	10	〈	〈	PROPN
ma-51	89	11	x	x	X
ma-51	89	12	−	−	PROPN
ma-51	89	13	z	z	PROPN
ma-51	89	14	,	,	PUNCT
ma-51	89	15	z	z	NOUN
ma-51	90	1	−	−	PROPN
ma-51	90	2	y	y	PROPN
ma-51	90	3	〉	〉	PROPN
ma-51	90	4	≥	≥	NOUN
ma-51	90	5	0,∀y	0,∀y	NUM
ma-51	91	1	∈	∈	PROPN
ma-51	91	2	k.	k.	PROPN
ma-51	91	3	definition	definition	NOUN
ma-51	91	4	2.2	2.2	NUM
ma-51	91	5	.	.	PUNCT
ma-51	92	1	the	the	DET
ma-51	92	2	banach	banach	NOUN
ma-51	92	3	space	space	NOUN
ma-51	92	4	z	z	NOUN
ma-51	92	5	is	be	AUX
ma-51	92	6	said	say	VERB
ma-51	92	7	to	to	PART
ma-51	92	8	have	have	VERB
ma-51	92	9	opial	opial	ADJ
ma-51	92	10	property	property	NOUN
ma-51	92	11	,	,	PUNCT
ma-51	92	12	if	if	SCONJ
ma-51	92	13	for	for	ADP
ma-51	92	14	each	each	DET
ma-51	92	15	weakly	weakly	ADJ
ma-51	92	16	convergent	convergent	ADJ
ma-51	92	17	sequence	sequence	NOUN
ma-51	92	18	{	{	PUNCT
ma-51	92	19	zn}∞n=0with	zn}∞n=0with	ADP
ma-51	92	20	weak	weak	ADJ
ma-51	92	21	limit	limit	NOUN
ma-51	92	22	z	z	X
ma-51	92	23	∈	∈	PROPN
ma-51	93	1	z	z	PROPN
ma-51	93	2	,	,	PUNCT
ma-51	93	3	the	the	DET
ma-51	93	4	following	follow	VERB
ma-51	93	5	inequality	inequality	NOUN
ma-51	93	6	holds	hold	VERB
ma-51	93	7	:	:	PUNCT
ma-51	93	8	lim	lim	PROPN
ma-51	93	9	sup	sup	VERB
ma-51	93	10	n→∞	n→∞	NUM
ma-51	94	1	‖zn	‖zn	NUM
ma-51	94	2	−	−	PROPN
ma-51	94	3	z‖	z‖	NOUN
ma-51	94	4	<	<	X
ma-51	95	1	‖zn	‖zn	NUM
ma-51	95	2	−	−	NOUN
ma-51	95	3	y‖,∀y	y‖,∀y	PRON
ma-51	95	4	∈	∈	NOUN
ma-51	95	5	zwithz	zwithz	NOUN
ma-51	95	6	6=	6=	ADP
ma-51	95	7	y	y	PROPN
ma-51	95	8	.	.	PUNCT
ma-51	96	1	note	note	VERB
ma-51	96	2	that	that	SCONJ
ma-51	96	3	all	all	DET
ma-51	96	4	finite	finite	ADJ
ma-51	96	5	dimensional	dimensional	ADJ
ma-51	96	6	banach	banach	NOUN
ma-51	96	7	spaces	space	NOUN
ma-51	96	8	,	,	PUNCT
ma-51	96	9	all	all	DET
ma-51	96	10	hilbert	hilbert	NOUN
ma-51	96	11	spaces	space	NOUN
ma-51	96	12	and	and	CCONJ
ma-51	96	13	`	`	PUNCT
ma-51	96	14	p(0	p(0	VERB
ma-51	96	15	≤	≤	NOUN
ma-51	96	16	p	p	NOUN
ma-51	96	17	<	<	X
ma-51	96	18	∞	∞	NOUN
ma-51	96	19	)	)	PUNCT
ma-51	96	20	satisfy	satisfy	VERB
ma-51	96	21	the	the	DET
ma-51	96	22	opial	opial	ADJ
ma-51	96	23	property	property	NOUN
ma-51	96	24	.	.	PUNCT
ma-51	97	1	but	but	CCONJ
ma-51	97	2	lp(1	lp(1	PROPN
ma-51	97	3	<	<	X
ma-51	97	4	p	p	X
ma-51	97	5	<	<	X
ma-51	97	6	∞.p	∞.p	NUM
ma-51	97	7	6=	6=	NOUN
ma-51	97	8	2	2	NUM
ma-51	97	9	)	)	PUNCT
ma-51	97	10	do	do	AUX
ma-51	97	11	not	not	PART
ma-51	97	12	satisfies	satisfy	VERB
ma-51	97	13	the	the	DET
ma-51	97	14	opial	opial	ADJ
ma-51	97	15	property	property	NOUN
ma-51	97	16	.	.	PUNCT
ma-51	98	1	definition	definition	NOUN
ma-51	98	2	2.3	2.3	NUM
ma-51	98	3	.	.	PUNCT
ma-51	99	1	(	(	PUNCT
ma-51	99	2	see	see	VERB
ma-51	99	3	[	[	X
ma-51	99	4	27	27	NUM
ma-51	99	5	]	]	PUNCT
ma-51	99	6	)	)	PUNCT
ma-51	99	7	let	let	VERB
ma-51	99	8	e	e	PRON
ma-51	99	9	be	be	AUX
ma-51	99	10	a	a	DET
ma-51	99	11	real	real	ADJ
ma-51	99	12	banach	banach	NOUN
ma-51	99	13	space	space	NOUN
ma-51	99	14	.	.	PUNCT
ma-51	100	1	a	a	DET
ma-51	100	2	mapping	mapping	NOUN
ma-51	100	3	t	t	PROPN
ma-51	100	4	,	,	PUNCT
ma-51	100	5	with	with	ADP
ma-51	100	6	domain	domain	NOUN
ma-51	100	7	d(t	d(t	PROPN
ma-51	100	8	)	)	PUNCT
ma-51	100	9	∈	∈	PROPN
ma-51	100	10	e	e	NOUN
ma-51	100	11	,	,	PUNCT
ma-51	100	12	is	be	AUX
ma-51	100	13	said	say	VERB
ma-51	100	14	to	to	PART
ma-51	100	15	be	be	AUX
ma-51	100	16	demiclosed	demiclose	VERB
ma-51	100	17	at	at	ADP
ma-51	100	18	0	0	NUM
ma-51	100	19	if	if	SCONJ
ma-51	100	20	for	for	ADP
ma-51	100	21	any	any	DET
ma-51	100	22	sequence	sequence	NOUN
ma-51	101	1	zn	zn	PROPN
ma-51	101	2	⊂	⊂	PROPN
ma-51	101	3	e	e	PROPN
ma-51	101	4	,	,	PUNCT
ma-51	101	5	zn	zn	PROPN
ma-51	101	6	�	�	PROPN
ma-51	101	7	q	q	PROPN
ma-51	101	8	∈	∈	PROPN
ma-51	101	9	d(t	d(t	PROPN
ma-51	101	10	)	)	PUNCT
ma-51	101	11	and	and	CCONJ
ma-51	101	12	‖zn−tzn‖	‖zn−tzn‖	ADJ
ma-51	101	13	→	→	SYM
ma-51	101	14	0	0	NUM
ma-51	101	15	,	,	PUNCT
ma-51	101	16	then	then	ADV
ma-51	101	17	tq	tq	ADP
ma-51	101	18	=	=	SYM
ma-51	101	19	q.	q.	PROPN
ma-51	101	20	lemma	lemma	PROPN
ma-51	101	21	2.1	2.1	NUM
ma-51	101	22	.	.	PUNCT
ma-51	102	1	(	(	PUNCT
ma-51	102	2	see	see	VERB
ma-51	102	3	[	[	X
ma-51	102	4	27	27	NUM
ma-51	102	5	]	]	PUNCT
ma-51	102	6	)	)	PUNCT
ma-51	102	7	let	let	VERB
ma-51	102	8	h	h	NOUN
ma-51	102	9	be	be	AUX
ma-51	102	10	a	a	DET
ma-51	102	11	real	real	ADJ
ma-51	102	12	hilbert	hilbert	NOUN
ma-51	102	13	space	space	NOUN
ma-51	102	14	.	.	PUNCT
ma-51	103	1	then	then	ADV
ma-51	103	2	,	,	PUNCT
ma-51	103	3	the	the	DET
ma-51	103	4	following	follow	VERB
ma-51	103	5	inequality	inequality	NOUN
ma-51	103	6	holds	hold	VERB
ma-51	103	7	:	:	PUNCT
ma-51	103	8	‖λx	‖λx	NUM
ma-51	103	9	+	+	CCONJ
ma-51	103	10	(	(	PUNCT
ma-51	103	11	1−	1−	NUM
ma-51	103	12	λ)y‖2	λ)y‖2	PROPN
ma-51	103	13	≤	≤	ADV
ma-51	103	14	λ‖x‖2	λ‖x‖2	PROPN
ma-51	103	15	+	+	CCONJ
ma-51	103	16	(	(	PUNCT
ma-51	103	17	1−	1−	NUM
ma-51	103	18	λ)‖y‖2	λ)‖y‖2	NOUN
ma-51	104	1	−	−	PROPN
ma-51	104	2	λ(1−	λ(1−	PROPN
ma-51	104	3	λ)‖x	λ)‖x	PROPN
ma-51	104	4	−	−	PROPN
ma-51	104	5	y‖,∀λ	y‖,∀λ	PROPN
ma-51	104	6	∈	∈	PROPN
ma-51	105	1	[	[	X
ma-51	105	2	0	0	NUM
ma-51	105	3	,	,	PUNCT
ma-51	105	4	1],∀x	1],∀x	NUM
ma-51	105	5	,	,	PUNCT
ma-51	105	6	y	y	PROPN
ma-51	105	7	∈	∈	PROPN
ma-51	105	8	h.	h.	PROPN
ma-51	105	9	lemma	lemma	PROPN
ma-51	105	10	2.2	2.2	NUM
ma-51	105	11	.	.	PUNCT
ma-51	106	1	(	(	PUNCT
ma-51	106	2	see	see	VERB
ma-51	106	3	[	[	X
ma-51	106	4	27	27	NUM
ma-51	106	5	]	]	PUNCT
ma-51	106	6	)	)	PUNCT
ma-51	106	7	let	let	VERB
ma-51	106	8	{	{	PUNCT
ma-51	106	9	sn}n∈n	sn}n∈n	INTJ
ma-51	106	10	be	be	AUX
ma-51	106	11	a	a	DET
ma-51	106	12	sequence	sequence	NOUN
ma-51	106	13	of	of	ADP
ma-51	106	14	nonnegative	nonnegative	ADJ
ma-51	106	15	real	real	ADJ
ma-51	106	16	numbers	number	NOUN
ma-51	106	17	satisfying	satisfy	VERB
ma-51	106	18	the	the	DET
ma-51	106	19	inequality	inequality	NOUN
ma-51	106	20	:	:	PUNCT
ma-51	106	21	sn+1	sn+1	VERB
ma-51	106	22	≤	≤	NUM
ma-51	106	23	(	(	PUNCT
ma-51	106	24	1−	1−	NUM
ma-51	106	25	γn)sn	γn)sn	PUNCT
ma-51	107	1	+	+	NUM
ma-51	107	2	δn,∀n	δn,∀n	NOUN
ma-51	107	3	≥	≥	NUM
ma-51	107	4	1	1	NUM
ma-51	107	5	,	,	PUNCT
ma-51	107	6	where	where	SCONJ
ma-51	107	7	{	{	PUNCT
ma-51	107	8	γn}n∈n	γn}n∈n	PUNCT
ma-51	107	9	and	and	CCONJ
ma-51	107	10	{	{	PUNCT
ma-51	107	11	δn}n∈n	δn}n∈n	INTJ
ma-51	107	12	satisfy	satisfy	VERB
ma-51	107	13	the	the	DET
ma-51	107	14	following	follow	VERB
ma-51	107	15	conditions:(i	conditions:(i	NOUN
ma-51	107	16	)	)	PUNCT
ma-51	107	17	{	{	PUNCT
ma-51	108	1	γn}n∈n	γn}n∈n	PUNCT
ma-51	108	2	⊂	⊂	PROPN
ma-51	108	3	(	(	PUNCT
ma-51	108	4	0	0	NUM
ma-51	108	5	,	,	PUNCT
ma-51	108	6	1);(ii	1);(ii	NUM
ma-51	108	7	)	)	PUNCT
ma-51	108	8	∑∞	∑∞	NOUN
ma-51	108	9	n=1	n=1	PUNCT
ma-51	108	10	γn	γn	ADP
ma-51	108	11	=	=	PROPN
ma-51	108	12	∞.	∞.	PROPN
ma-51	108	13	suppose	suppose	VERB
ma-51	108	14	∑∞	∑∞	NOUN
ma-51	108	15	n=1	n=1	PUNCT
ma-51	108	16	δn	δn	ADP
ma-51	108	17	<	<	PROPN
ma-51	108	18	∞	∞	PROPN
ma-51	108	19	,	,	PUNCT
ma-51	108	20	then	then	ADV
ma-51	108	21	,	,	PUNCT
ma-51	108	22	limn→∞	limn→∞	PROPN
ma-51	108	23	sn	sn	X
ma-51	108	24	=	=	SYM
ma-51	108	25	0	0	PROPN
ma-51	108	26	.	.	PUNCT
ma-51	109	1	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	109	2	eur	eur	PROPN
ma-51	109	3	.	.	PUNCT
ma-51	110	1	j.	j.	PROPN
ma-51	110	2	math	math	PROPN
ma-51	110	3	.	.	PUNCT
ma-51	111	1	anal	anal	PROPN
ma-51	111	2	.	.	PUNCT
ma-51	112	1	10.28924	10.28924	NUM
ma-51	112	2	/	/	SYM
ma-51	112	3	ada	ada	PROPN
ma-51	112	4	/	/	SYM
ma-51	112	5	ma.2.10	ma.2.10	PROPN
ma-51	112	6	5	5	NUM
ma-51	112	7	lemma	lemma	PROPN
ma-51	112	8	2.3	2.3	NUM
ma-51	112	9	.	.	PUNCT
ma-51	113	1	(	(	PUNCT
ma-51	113	2	see	see	VERB
ma-51	113	3	[	[	X
ma-51	113	4	4	4	NUM
ma-51	113	5	]	]	PUNCT
ma-51	113	6	)	)	PUNCT
ma-51	113	7	let	let	VERB
ma-51	113	8	e	e	PRON
ma-51	113	9	be	be	AUX
ma-51	113	10	a	a	DET
ma-51	113	11	real	real	ADJ
ma-51	113	12	hilbert	hilbert	NOUN
ma-51	113	13	space	space	NOUN
ma-51	113	14	.	.	PUNCT
ma-51	114	1	then	then	ADV
ma-51	114	2	,	,	PUNCT
ma-51	114	3	for	for	ADP
ma-51	114	4	all	all	DET
ma-51	114	5	x	x	NOUN
ma-51	114	6	,	,	PUNCT
ma-51	114	7	y	y	PROPN
ma-51	114	8	∈	∈	PROPN
ma-51	114	9	h	h	NOUN
ma-51	114	10	,	,	PUNCT
ma-51	114	11	the	the	DET
ma-51	114	12	following	follow	VERB
ma-51	114	13	inequalities	inequality	NOUN
ma-51	114	14	hold	hold	VERB
ma-51	114	15	:	:	PUNCT
ma-51	114	16	i.	i.	PROPN
ma-51	114	17	‖x	‖x	PROPN
ma-51	115	1	−	−	PROPN
ma-51	115	2	y‖2	y‖2	PROPN
ma-51	115	3	≤	≤	PROPN
ma-51	115	4	‖x‖2	‖x‖2	VERB
ma-51	115	5	−	−	PROPN
ma-51	115	6	2〈y	2〈y	ADV
ma-51	115	7	,	,	PUNCT
ma-51	115	8	(	(	PUNCT
ma-51	115	9	x	x	X
ma-51	116	1	+	+	NUM
ma-51	116	2	y)〉+	y)〉+	NUM
ma-51	116	3	‖y‖2	‖y‖2	PROPN
ma-51	116	4	;	;	PUNCT
ma-51	116	5	ii	ii	X
ma-51	116	6	.	.	PUNCT
ma-51	117	1	‖x	‖x	NOUN
ma-51	118	1	−	−	PROPN
ma-51	118	2	y‖2	y‖2	PROPN
ma-51	118	3	≤	≤	PROPN
ma-51	118	4	‖x‖2	‖x‖2	VERB
ma-51	118	5	−	−	PROPN
ma-51	118	6	2〈y	2〈y	ADV
ma-51	118	7	,	,	PUNCT
ma-51	118	8	(	(	PUNCT
ma-51	118	9	x	x	X
ma-51	118	10	+	+	NUM
ma-51	118	11	y	y	NOUN
ma-51	118	12	)	)	PUNCT
ma-51	118	13	〉	〉	PROPN
ma-51	118	14	.	.	PUNCT
ma-51	119	1	lemma	lemma	PROPN
ma-51	119	2	2.4	2.4	NUM
ma-51	119	3	.	.	PUNCT
ma-51	120	1	(	(	PUNCT
ma-51	120	2	see	see	VERB
ma-51	120	3	[	[	X
ma-51	120	4	?	?	PUNCT
ma-51	120	5	]	]	X
ma-51	120	6	)	)	PUNCT
ma-51	120	7	let	let	VERB
ma-51	120	8	d	d	PRON
ma-51	120	9	be	be	AUX
ma-51	120	10	a	a	DET
ma-51	120	11	sunset	sunset	NOUN
ma-51	120	12	of	of	ADP
ma-51	120	13	a	a	DET
ma-51	120	14	real	real	ADJ
ma-51	120	15	hilbert	hilbert	NOUN
ma-51	120	16	space	space	NOUN
ma-51	120	17	,	,	PUNCT
ma-51	120	18	t	t	NOUN
ma-51	120	19	:	:	PUNCT
ma-51	120	20	d	d	X
ma-51	120	21	−→	−→	NOUN
ma-51	120	22	h	h	NOUN
ma-51	120	23	be	be	VERB
ma-51	120	24	a	a	DET
ma-51	120	25	nonexpansive	nonexpansive	ADJ
ma-51	120	26	mapping	mapping	NOUN
ma-51	120	27	and	and	CCONJ
ma-51	120	28	z	z	NOUN
ma-51	120	29	a	a	DET
ma-51	120	30	weak	weak	ADJ
ma-51	120	31	cluster	cluster	NOUN
ma-51	120	32	point	point	NOUN
ma-51	120	33	of	of	ADP
ma-51	120	34	the	the	DET
ma-51	120	35	sequence	sequence	NOUN
ma-51	120	36	{	{	PUNCT
ma-51	120	37	yn}∞n=0	yn}∞n=0	NUM
ma-51	120	38	.	.	PROPN
ma-51	121	1	if	if	SCONJ
ma-51	121	2	‖tyn	‖tyn	PRON
ma-51	121	3	−	−	NOUN
ma-51	121	4	yn‖	yn‖	NOUN
ma-51	121	5	→	→	SYM
ma-51	121	6	0	0	NUM
ma-51	121	7	,	,	PUNCT
ma-51	121	8	then	then	ADV
ma-51	121	9	z	z	PROPN
ma-51	121	10	∈	∈	PROPN
ma-51	121	11	f	f	X
ma-51	121	12	(	(	PUNCT
ma-51	121	13	t	t	NOUN
ma-51	121	14	)	)	PUNCT
ma-51	121	15	proposition	proposition	NOUN
ma-51	121	16	2.5	2.5	NUM
ma-51	121	17	.	.	PUNCT
ma-51	122	1	(	(	PUNCT
ma-51	122	2	see	see	VERB
ma-51	122	3	[	[	X
ma-51	122	4	27	27	NUM
ma-51	122	5	]	]	PUNCT
ma-51	122	6	)	)	PUNCT
ma-51	122	7	let	let	VERB
ma-51	122	8	d	d	PRON
ma-51	122	9	be	be	AUX
ma-51	122	10	a	a	DET
ma-51	122	11	nonempty	nonempty	ADJ
ma-51	122	12	subset	subset	NOUN
ma-51	122	13	of	of	ADP
ma-51	122	14	a	a	DET
ma-51	122	15	real	real	ADJ
ma-51	122	16	hilbert	hilbert	NOUN
ma-51	122	17	space	space	NOUN
ma-51	122	18	amd	amd	PROPN
ma-51	122	19	γ	γ	X
ma-51	122	20	:	:	PUNCT
ma-51	122	21	d	d	X
ma-51	122	22	−→	−→	NOUN
ma-51	122	23	d	d	X
ma-51	122	24	an	an	DET
ma-51	122	25	α	α	X
ma-51	122	26	-	-	PUNCT
ma-51	122	27	demicontractive	demicontractive	ADJ
ma-51	122	28	mapping	mapping	NOUN
ma-51	122	29	.	.	PUNCT
ma-51	123	1	assume	assume	VERB
ma-51	123	2	that	that	SCONJ
ma-51	123	3	x	x	SYM
ma-51	123	4	∈	∈	PROPN
ma-51	123	5	d	d	NOUN
ma-51	123	6	and	and	CCONJ
ma-51	123	7	α	α	PRON
ma-51	123	8	≥	≥	NUM
ma-51	123	9	1	1	NUM
ma-51	123	10	.	.	PUNCT
ma-51	124	1	then	then	ADV
ma-51	124	2	,	,	PUNCT
ma-51	124	3	γ	γ	X
ma-51	124	4	is	be	AUX
ma-51	124	5	lipschitizian	lipschitizian	PROPN
ma-51	124	6	.	.	PUNCT
ma-51	125	1	theorem	theorem	VERB
ma-51	125	2	2.6	2.6	NUM
ma-51	125	3	.	.	PUNCT
ma-51	126	1	(	(	PUNCT
ma-51	126	2	see	see	VERB
ma-51	126	3	[	[	X
ma-51	126	4	4	4	NUM
ma-51	126	5	]	]	PUNCT
ma-51	126	6	)	)	PUNCT
ma-51	126	7	a	a	DET
ma-51	126	8	banach	banach	NOUN
ma-51	126	9	space	space	NOUN
ma-51	126	10	e	e	NOUN
ma-51	126	11	is	be	AUX
ma-51	126	12	reflexive	reflexive	ADJ
ma-51	126	13	if	if	SCONJ
ma-51	126	14	and	and	CCONJ
ma-51	126	15	only	only	ADV
ma-51	126	16	if	if	SCONJ
ma-51	126	17	every	every	DET
ma-51	126	18	(	(	PUNCT
ma-51	126	19	normed	normed	PROPN
ma-51	126	20	)	)	PUNCT
ma-51	126	21	bounded	bound	VERB
ma-51	126	22	sequence	sequence	NOUN
ma-51	126	23	in	in	ADP
ma-51	126	24	e	e	PROPN
ma-51	126	25	has	have	VERB
ma-51	126	26	a	a	DET
ma-51	126	27	subsequence	subsequence	NOUN
ma-51	126	28	which	which	PRON
ma-51	126	29	converges	converge	VERB
ma-51	126	30	weakly	weakly	ADJ
ma-51	126	31	to	to	ADP
ma-51	126	32	an	an	DET
ma-51	126	33	element	element	NOUN
ma-51	126	34	of	of	ADP
ma-51	126	35	e.	e.	PROPN
ma-51	126	36	3	3	PROPN
ma-51	126	37	.	.	PUNCT
ma-51	126	38	convergence	convergence	NOUN
ma-51	126	39	results	result	NOUN
ma-51	126	40	now	now	ADV
ma-51	126	41	,	,	PUNCT
ma-51	126	42	we	we	PRON
ma-51	126	43	prove	prove	VERB
ma-51	126	44	our	our	PRON
ma-51	126	45	main	main	ADJ
ma-51	126	46	results	result	NOUN
ma-51	126	47	.	.	PUNCT
ma-51	127	1	theorem	theorem	VERB
ma-51	127	2	3.1	3.1	NUM
ma-51	127	3	.	.	PUNCT
ma-51	128	1	let	let	VERB
ma-51	128	2	h	h	PRON
ma-51	128	3	be	be	AUX
ma-51	128	4	a	a	DET
ma-51	128	5	real	real	ADJ
ma-51	128	6	hilbert	hilbert	NOUN
ma-51	128	7	space	space	NOUN
ma-51	128	8	,	,	PUNCT
ma-51	128	9	k	k	PROPN
ma-51	128	10	a	a	DET
ma-51	128	11	nonempty	nonempty	ADV
ma-51	128	12	closed	close	VERB
ma-51	128	13	convex	convex	NOUN
ma-51	128	14	subset	subset	NOUN
ma-51	128	15	of	of	ADP
ma-51	128	16	h	h	PROPN
ma-51	128	17	and	and	CCONJ
ma-51	128	18	t	t	PROPN
ma-51	128	19	:	:	PUNCT
ma-51	129	1	k	k	X
ma-51	129	2	−→	−→	NOUN
ma-51	129	3	k	k	PROPN
ma-51	129	4	an	an	DET
ma-51	129	5	l	l	NOUN
ma-51	129	6	-	-	ADJ
ma-51	129	7	lipschitz	lipschitz	ADJ
ma-51	129	8	α	α	NOUN
ma-51	129	9	-	-	ADJ
ma-51	129	10	hemicontractive	hemicontractive	ADJ
ma-51	129	11	mapping	mapping	NOUN
ma-51	129	12	.	.	PUNCT
ma-51	130	1	for	for	ADP
ma-51	130	2	any	any	DET
ma-51	130	3	arbitrary	arbitrary	ADJ
ma-51	130	4	x0	x0	PROPN
ma-51	130	5	∈	∈	PROPN
ma-51	130	6	h	h	NOUN
ma-51	130	7	,	,	PUNCT
ma-51	130	8	define	define	VERB
ma-51	130	9	the	the	DET
ma-51	130	10	sequence	sequence	NOUN
ma-51	130	11	{	{	PUNCT
ma-51	130	12	xn}∞n=0	xn}∞n=0	X
ma-51	130	13	iteratively	iteratively	ADV
ma-51	130	14	as	as	ADP
ma-51	130	15	follows:	follows:	NOUN
ma-51	130	16	xn+1	xn+1	PROPN
ma-51	131	1	=	=	PUNCT
ma-51	132	1	pk[(1−	pk[(1−	PROPN
ma-51	132	2	αn	αn	ADP
ma-51	133	1	−	−	PROPN
ma-51	133	2	γn)xn	γn)xn	PROPN
ma-51	133	3	+	+	CCONJ
ma-51	133	4	γntyn	γntyn	PROPN
ma-51	133	5	]	]	X
ma-51	133	6	yn	yn	PROPN
ma-51	133	7	=	=	SYM
ma-51	133	8	(	(	PUNCT
ma-51	133	9	1−	1−	NUM
ma-51	133	10	βn)xn	βn)xn	PROPN
ma-51	133	11	+	+	CCONJ
ma-51	133	12	βntxn	βntxn	ADJ
ma-51	133	13	,	,	PUNCT
ma-51	133	14	n	n	PRON
ma-51	133	15	≥	≥	NOUN
ma-51	133	16	1	1	NUM
ma-51	133	17	,	,	PUNCT
ma-51	133	18	(	(	PUNCT
ma-51	133	19	3.1	3.1	NUM
ma-51	133	20	)	)	PUNCT
ma-51	133	21	where	where	SCONJ
ma-51	133	22	the	the	DET
ma-51	133	23	sequences	sequence	NOUN
ma-51	133	24	{	{	PUNCT
ma-51	133	25	δn}∞n=0	δn}∞n=0	X
ma-51	133	26	,	,	PUNCT
ma-51	133	27	{	{	PUNCT
ma-51	133	28	γn}∞n=0	γn}∞n=0	VERB
ma-51	133	29	,	,	PUNCT
ma-51	133	30	{	{	PUNCT
ma-51	133	31	βn}∞n=0	βn}∞n=0	X
ma-51	133	32	∈	∈	PROPN
ma-51	133	33	(	(	PUNCT
ma-51	133	34	0	0	NUM
ma-51	133	35	,	,	PUNCT
ma-51	133	36	1	1	X
ma-51	133	37	)	)	PUNCT
ma-51	133	38	satisfy	satisfy	VERB
ma-51	133	39	the	the	DET
ma-51	133	40	following	follow	VERB
ma-51	133	41	conditions	condition	NOUN
ma-51	133	42	:	:	PUNCT
ma-51	133	43	(	(	PUNCT
ma-51	133	44	i	i	NOUN
ma-51	133	45	)	)	PUNCT
ma-51	133	46	0	0	PUNCT
ma-51	133	47	<	<	X
ma-51	133	48	δ	δ	PROPN
ma-51	133	49	≤	≤	NUM
ma-51	133	50	δn	δn	ADJ
ma-51	133	51	≤	≤	NUM
ma-51	133	52	βn	βn	NOUN
ma-51	133	53	≤	≤	NUM
ma-51	133	54	γn	γn	ADP
ma-51	133	55	≤	≤	NUM
ma-51	133	56	γ	γ	X
ma-51	133	57	≤	≤	NOUN
ma-51	133	58	1−	1−	NUM
ma-51	133	59	δ	δ	NOUN
ma-51	133	60	1	1	NUM
ma-51	133	61	+	+	CCONJ
ma-51	133	62	l2	l2	NOUN
ma-51	133	63	;	;	PUNCT
ma-51	133	64	(	(	PUNCT
ma-51	134	1	i	i	PRON
ma-51	134	2	i	i	PROPN
ma-51	134	3	)	)	PUNCT
ma-51	134	4	limn→∞	limn→∞	VERB
ma-51	134	5	δn	δn	NOUN
ma-51	134	6	=	=	SYM
ma-51	134	7	0	0	NUM
ma-51	134	8	and	and	CCONJ
ma-51	134	9	∑∞	∑∞	NOUN
ma-51	134	10	n=0	n=0	X
ma-51	134	11	δn	δn	NOUN
ma-51	134	12	=	=	SYM
ma-51	134	13	∞.	∞.	PROPN
ma-51	134	14	then	then	ADV
ma-51	134	15	,	,	PUNCT
ma-51	134	16	the	the	DET
ma-51	134	17	sequence	sequence	NOUN
ma-51	134	18	{	{	PUNCT
ma-51	134	19	xn}∞n=0	xn}∞n=0	VERB
ma-51	134	20	generated	generate	VERB
ma-51	134	21	by	by	ADP
ma-51	134	22	(	(	PUNCT
ma-51	134	23	3.1	3.1	NUM
ma-51	134	24	)	)	PUNCT
ma-51	134	25	weakly	weakly	ADJ
ma-51	134	26	and	and	CCONJ
ma-51	134	27	strongly	strongly	ADV
ma-51	134	28	converges	converge	VERB
ma-51	134	29	to	to	ADP
ma-51	134	30	the	the	DET
ma-51	134	31	fixed	fix	VERB
ma-51	134	32	point	point	NOUN
ma-51	134	33	of	of	ADP
ma-51	134	34	t	t	PROPN
ma-51	134	35	.	.	PUNCT
ma-51	135	1	proof	proof	NOUN
ma-51	135	2	.	.	PUNCT
ma-51	136	1	since	since	SCONJ
ma-51	136	2	f	f	PROPN
ma-51	136	3	(	(	PUNCT
ma-51	136	4	t	t	PROPN
ma-51	136	5	)	)	PUNCT
ma-51	136	6	is	be	AUX
ma-51	136	7	nonempty	nonempty	ADJ
ma-51	136	8	,	,	PUNCT
ma-51	136	9	let	let	VERB
ma-51	136	10	αq	αq	ADP
ma-51	136	11	∈	∈	PROPN
ma-51	136	12	f	f	X
ma-51	136	13	(	(	PUNCT
ma-51	136	14	t	t	PROPN
ma-51	136	15	)	)	PUNCT
ma-51	136	16	and	and	CCONJ
ma-51	136	17	x	x	PUNCT
ma-51	136	18	∈	∈	PROPN
ma-51	136	19	k.	k.	NOUN
ma-51	136	20	using	use	VERB
ma-51	136	21	(	(	PUNCT
ma-51	136	22	3.1	3.1	NUM
ma-51	136	23	)	)	PUNCT
ma-51	136	24	,	,	PUNCT
ma-51	136	25	lemma	lemma	PROPN
ma-51	136	26	2.1	2.1	NUM
ma-51	136	27	and	and	CCONJ
ma-51	136	28	the	the	DET
ma-51	136	29	factthat	factthat	PROPN
ma-51	136	30	t	t	PROPN
ma-51	136	31	is	be	AUX
ma-51	136	32	l	l	NOUN
ma-51	136	33	-	-	NOUN
ma-51	136	34	lipschitizian	lipschitizian	ADJ
ma-51	136	35	,	,	PUNCT
ma-51	136	36	we	we	PRON
ma-51	136	37	estimate	estimate	VERB
ma-51	136	38	as	as	SCONJ
ma-51	136	39	follows	follow	VERB
ma-51	136	40	:	:	PUNCT
ma-51	136	41	‖xn+1	‖xn+1	NUM
ma-51	137	1	−	−	PRON
ma-51	137	2	αq‖2	αq‖2	PROPN
ma-51	137	3	=	=	PUNCT
ma-51	137	4	‖pk[(1−	‖pk[(1−	NOUN
ma-51	137	5	δn	δn	ADP
ma-51	137	6	−	−	X
ma-51	137	7	γn)xn	γn)xn	PROPN
ma-51	137	8	+	+	CCONJ
ma-51	137	9	γntyn]−	γntyn]−	VERB
ma-51	137	10	αq‖	αq‖	NOUN
ma-51	137	11	≤	≤	NUM
ma-51	137	12	‖(1−	‖(1−	PROPN
ma-51	137	13	δn	δn	NOUN
ma-51	137	14	−	−	X
ma-51	137	15	γn)xn	γn)xn	PROPN
ma-51	137	16	+	+	CCONJ
ma-51	137	17	γntyn	γntyn	NOUN
ma-51	137	18	−	−	PROPN
ma-51	137	19	αq‖	αq‖	NOUN
ma-51	137	20	=	=	SYM
ma-51	137	21	‖(1−	‖(1−	PROPN
ma-51	137	22	δn	δn	NOUN
ma-51	137	23	−	−	PROPN
ma-51	137	24	γn)(xn	γn)(xn	PUNCT
ma-51	137	25	−	−	PROPN
ma-51	137	26	αq	αq	NUM
ma-51	137	27	)	)	PUNCT
ma-51	137	28	+	+	CCONJ
ma-51	137	29	γn(tyn	γn(tyn	ADJ
ma-51	137	30	−	−	PROPN
ma-51	137	31	αq)−	αq)−	PROPN
ma-51	137	32	δnαq‖	δnαq‖	NUM
ma-51	137	33	≤	≤	NUM
ma-51	137	34	‖(1−	‖(1−	NUM
ma-51	137	35	δn	δn	NOUN
ma-51	137	36	−	−	PROPN
ma-51	137	37	γn)(xn	γn)(xn	PUNCT
ma-51	137	38	−	−	PROPN
ma-51	137	39	αq	αq	NUM
ma-51	137	40	)	)	PUNCT
ma-51	137	41	+	+	CCONJ
ma-51	137	42	γn(tyn	γn(tyn	PROPN
ma-51	137	43	−	−	PROPN
ma-51	137	44	αq)‖+	αq)‖+	PROPN
ma-51	137	45	δn‖αq‖.	δn‖αq‖.	PUNCT
ma-51	137	46	(	(	PUNCT
ma-51	137	47	3.2	3.2	NUM
ma-51	137	48	)	)	PUNCT
ma-51	137	49	set	set	VERB
ma-51	137	50	qn	qn	NOUN
ma-51	137	51	=	=	SYM
ma-51	137	52	‖(1−	‖(1−	PROPN
ma-51	137	53	δn	δn	NOUN
ma-51	137	54	−	−	PROPN
ma-51	137	55	γn)(xn	γn)(xn	PUNCT
ma-51	137	56	−	−	PROPN
ma-51	137	57	αq	αq	NUM
ma-51	137	58	)	)	PUNCT
ma-51	138	1	+	+	CCONJ
ma-51	138	2	γn(tyn	γn(tyn	PROPN
ma-51	138	3	−	−	PROPN
ma-51	138	4	αq)‖2	αq)‖2	NOUN
ma-51	138	5	and	and	CCONJ
ma-51	138	6	observe	observe	VERB
ma-51	138	7	that	that	SCONJ
ma-51	138	8	qn	qn	NOUN
ma-51	138	9	=	=	PUNCT
ma-51	138	10	‖(1−	‖(1−	X
ma-51	138	11	δn)(xn	δn)(xn	PUNCT
ma-51	138	12	−	−	PROPN
ma-51	138	13	αq)−	αq)−	X
ma-51	138	14	(	(	PUNCT
ma-51	138	15	1−	1−	NUM
ma-51	138	16	γn)(xn	γn)(xn	PUNCT
ma-51	138	17	−	−	PROPN
ma-51	138	18	αq	αq	NUM
ma-51	138	19	)	)	PUNCT
ma-51	139	1	+	+	CCONJ
ma-51	139	2	γn(tyn	γn(tyn	ADP
ma-51	139	3	−	−	PROPN
ma-51	139	4	αq)‖2	αq)‖2	PROPN
ma-51	139	5	.	.	PUNCT
ma-51	140	1	(	(	PUNCT
ma-51	140	2	3.3	3.3	NUM
ma-51	140	3	)	)	PUNCT
ma-51	140	4	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	140	5	eur	eur	PROPN
ma-51	140	6	.	.	PUNCT
ma-51	141	1	j.	j.	PROPN
ma-51	141	2	math	math	PROPN
ma-51	141	3	.	.	PUNCT
ma-51	142	1	anal	anal	PROPN
ma-51	142	2	.	.	PUNCT
ma-51	143	1	10.28924	10.28924	NUM
ma-51	143	2	/	/	SYM
ma-51	143	3	ada	ada	PROPN
ma-51	143	4	/	/	SYM
ma-51	143	5	ma.2.10	ma.2.10	PROPN
ma-51	143	6	6since	6since	NUM
ma-51	143	7	(	(	PUNCT
ma-51	143	8	1−	1−	NUM
ma-51	143	9	δn)(xn	δn)(xn	PUNCT
ma-51	143	10	−	−	PROPN
ma-51	143	11	αq	αq	NUM
ma-51	143	12	)	)	PUNCT
ma-51	143	13	=	=	SYM
ma-51	143	14	(	(	PUNCT
ma-51	143	15	1−	1−	NUM
ma-51	143	16	δn)(1−	δn)(1−	PROPN
ma-51	143	17	γn)(xn	γn)(xn	PUNCT
ma-51	143	18	−	−	PROPN
ma-51	143	19	αq	αq	NUM
ma-51	143	20	)	)	PUNCT
ma-51	144	1	+	+	CCONJ
ma-51	144	2	γn(1−	γn(1−	NUM
ma-51	144	3	δn))(xn	δn))(xn	PROPN
ma-51	144	4	−	−	PROPN
ma-51	144	5	αq	αq	NOUN
ma-51	144	6	)	)	PUNCT
ma-51	144	7	(	(	PUNCT
ma-51	144	8	3.4	3.4	NUM
ma-51	144	9	)	)	PUNCT
ma-51	144	10	and	and	CCONJ
ma-51	144	11	γn(tyn	γn(tyn	ADP
ma-51	144	12	−	−	PROPN
ma-51	145	1	αq	αq	ADP
ma-51	145	2	)	)	PUNCT
ma-51	145	3	=	=	PUNCT
ma-51	146	1	γn(1−	γn(1−	ADP
ma-51	146	2	δn)(tyn	δn)(tyn	NUM
ma-51	146	3	−	−	NOUN
ma-51	146	4	αq	αq	X
ma-51	146	5	)	)	PUNCT
ma-51	146	6	+	+	NUM
ma-51	146	7	γnδn(tyn	γnδn(tyn	NOUN
ma-51	146	8	−	−	NOUN
ma-51	146	9	αq	αq	NOUN
ma-51	146	10	)	)	PUNCT
ma-51	146	11	,	,	PUNCT
ma-51	146	12	(	(	PUNCT
ma-51	146	13	3.5	3.5	NUM
ma-51	146	14	)	)	PUNCT
ma-51	146	15	it	it	PRON
ma-51	146	16	follows	follow	VERB
ma-51	146	17	from	from	ADP
ma-51	146	18	(	(	PUNCT
ma-51	146	19	3.3	3.3	NUM
ma-51	146	20	)	)	PUNCT
ma-51	147	1	that	that	SCONJ
ma-51	147	2	qn	qn	NOUN
ma-51	147	3	=	=	PUNCT
ma-51	147	4	‖(1−	‖(1−	PROPN
ma-51	147	5	δn)(1−	δn)(1−	PROPN
ma-51	147	6	γn)(xn	γn)(xn	PUNCT
ma-51	147	7	−	−	PROPN
ma-51	147	8	αq	αq	NUM
ma-51	147	9	)	)	PUNCT
ma-51	147	10	+	+	CCONJ
ma-51	147	11	γn(1−	γn(1−	NUM
ma-51	147	12	δn))(xn	δn))(xn	PROPN
ma-51	147	13	−	−	PROPN
ma-51	147	14	αq)−	αq)−	PROPN
ma-51	147	15	(	(	PUNCT
ma-51	147	16	1−	1−	NUM
ma-51	147	17	γn)(xn	γn)(xn	PUNCT
ma-51	147	18	−	−	PROPN
ma-51	147	19	αq	αq	X
ma-51	147	20	)	)	PUNCT
ma-51	148	1	+	+	ADP
ma-51	148	2	γn(1−	γn(1−	NOUN
ma-51	148	3	δn)(tyn	δn)(tyn	NUM
ma-51	148	4	−	−	NOUN
ma-51	148	5	αq	αq	X
ma-51	148	6	)	)	PUNCT
ma-51	148	7	+	+	NUM
ma-51	148	8	γnδn(tyn	γnδn(tyn	NOUN
ma-51	148	9	−	−	NOUN
ma-51	148	10	αq)‖2	αq)‖2	NOUN
ma-51	148	11	=	=	X
ma-51	148	12	‖(1−	‖(1−	PROPN
ma-51	148	13	δn)[(1−	δn)[(1−	PROPN
ma-51	148	14	γn)(xn	γn)(xn	PUNCT
ma-51	148	15	−	−	PROPN
ma-51	148	16	αq	αq	NUM
ma-51	148	17	)	)	PUNCT
ma-51	148	18	+	+	CCONJ
ma-51	148	19	γn(tyn	γn(tyn	ADP
ma-51	148	20	−	−	PROPN
ma-51	148	21	αq	αq	ADP
ma-51	148	22	)	)	PUNCT
ma-51	148	23	]	]	PUNCT
ma-51	149	1	+	+	CCONJ
ma-51	149	2	δnγn(tyn	δnγn(tyn	NOUN
ma-51	149	3	−	−	PROPN
ma-51	149	4	xn)‖2	xn)‖2	PROPN
ma-51	149	5	.	.	PUNCT
ma-51	150	1	(	(	PUNCT
ma-51	150	2	3.6	3.6	NUM
ma-51	150	3	)	)	PUNCT
ma-51	150	4	(	(	PUNCT
ma-51	150	5	3.6	3.6	NUM
ma-51	150	6	)	)	PUNCT
ma-51	150	7	and	and	CCONJ
ma-51	150	8	lemma	lemma	PROPN
ma-51	150	9	2.1	2.1	NUM
ma-51	150	10	imply	imply	NOUN
ma-51	150	11	that	that	SCONJ
ma-51	150	12	qn	qn	NOUN
ma-51	150	13	=	=	X
ma-51	150	14	(	(	PUNCT
ma-51	150	15	1−	1−	NUM
ma-51	150	16	δn)‖(1−	δn)‖(1−	NUM
ma-51	150	17	γn)(xn	γn)(xn	PUNCT
ma-51	150	18	−	−	PROPN
ma-51	150	19	αq	αq	X
ma-51	150	20	)	)	PUNCT
ma-51	151	1	+	+	CCONJ
ma-51	151	2	γn(tyn	γn(tyn	ADP
ma-51	151	3	−	−	PROPN
ma-51	151	4	αq)‖2	αq)‖2	NOUN
ma-51	151	5	+	+	PROPN
ma-51	151	6	δn‖γn(tyn	δn‖γn(tyn	NOUN
ma-51	151	7	−	−	NOUN
ma-51	151	8	xn)‖2	xn)‖2	PROPN
ma-51	152	1	−δn(1−	−δn(1−	PROPN
ma-51	152	2	δn)‖xn	δn)‖xn	VERB
ma-51	152	3	−	−	PROPN
ma-51	152	4	αq‖2	αq‖2	PROPN
ma-51	152	5	.	.	PUNCT
ma-51	153	1	(	(	PUNCT
ma-51	153	2	3.7	3.7	NUM
ma-51	153	3	)	)	PUNCT
ma-51	153	4	if	if	SCONJ
ma-51	153	5	we	we	PRON
ma-51	153	6	denote	denote	VERB
ma-51	153	7	vn	vn	PROPN
ma-51	153	8	=	=	SYM
ma-51	153	9	‖(1−	‖(1−	PROPN
ma-51	153	10	γn)(xn	γn)(xn	SYM
ma-51	153	11	−αq	−αq	ADJ
ma-51	153	12	)	)	PUNCT
ma-51	153	13	+	+	CCONJ
ma-51	153	14	γn(tyn	γn(tyn	ADJ
ma-51	153	15	−αq)‖2	−αq)‖2	NOUN
ma-51	153	16	and	and	CCONJ
ma-51	153	17	use	use	VERB
ma-51	153	18	similar	similar	ADJ
ma-51	153	19	technique	technique	NOUN
ma-51	153	20	as	as	ADP
ma-51	153	21	above	above	ADV
ma-51	153	22	,	,	PUNCT
ma-51	153	23	thenwe	thenwe	PROPN
ma-51	153	24	get	get	VERB
ma-51	153	25	vn	vn	NOUN
ma-51	153	26	=	=	SYM
ma-51	153	27	(	(	PUNCT
ma-51	153	28	1−	1−	NUM
ma-51	153	29	γn)‖xn	γn)‖xn	NOUN
ma-51	153	30	−	−	NOUN
ma-51	154	1	αq‖2	αq‖2	NOUN
ma-51	154	2	+	+	CCONJ
ma-51	154	3	γn‖tyn	γn‖tyn	NOUN
ma-51	154	4	−	−	NOUN
ma-51	154	5	αq‖2	αq‖2	PROPN
ma-51	154	6	−	−	PROPN
ma-51	155	1	γn(1−	γn(1−	PROPN
ma-51	155	2	γn)‖xn	γn)‖xn	NOUN
ma-51	155	3	−	−	PROPN
ma-51	155	4	tyn‖2	tyn‖2	PROPN
ma-51	155	5	.	.	PUNCT
ma-51	156	1	(	(	PUNCT
ma-51	156	2	3.8	3.8	NUM
ma-51	156	3	)	)	PUNCT
ma-51	156	4	(	(	PUNCT
ma-51	156	5	3.7	3.7	NUM
ma-51	156	6	)	)	PUNCT
ma-51	156	7	and	and	CCONJ
ma-51	156	8	(	(	PUNCT
ma-51	156	9	3.8	3.8	NUM
ma-51	156	10	)	)	PUNCT
ma-51	156	11	imply	imply	VERB
ma-51	156	12	qn	qn	NOUN
ma-51	156	13	=	=	X
ma-51	156	14	(	(	PUNCT
ma-51	156	15	1−	1−	NUM
ma-51	156	16	δn)[(1−	δn)[(1−	PROPN
ma-51	156	17	γn)‖xn	γn)‖xn	PROPN
ma-51	156	18	−	−	NOUN
ma-51	157	1	αq‖2	αq‖2	NOUN
ma-51	157	2	+	+	CCONJ
ma-51	157	3	γn‖tyn	γn‖tyn	NOUN
ma-51	157	4	−	−	NOUN
ma-51	157	5	αq‖2	αq‖2	PROPN
ma-51	157	6	−	−	PROPN
ma-51	158	1	γn(1−	γn(1−	PROPN
ma-51	158	2	γn)‖xn	γn)‖xn	NOUN
ma-51	158	3	−	−	PROPN
ma-51	158	4	tyn‖2	tyn‖2	PRON
ma-51	158	5	]	]	PUNCT
ma-51	159	1	+	+	X
ma-51	159	2	δnγ	δnγ	NOUN
ma-51	159	3	2	2	NUM
ma-51	159	4	n‖tyn	n‖tyn	ADV
ma-51	159	5	−	−	PROPN
ma-51	159	6	xn‖2	xn‖2	PROPN
ma-51	159	7	−	−	PROPN
ma-51	159	8	δn(1−	δn(1−	PROPN
ma-51	159	9	δn)‖xn	δn)‖xn	NOUN
ma-51	159	10	−	−	NOUN
ma-51	159	11	αq‖2	αq‖2	NOUN
ma-51	159	12	=	=	PUNCT
ma-51	159	13	(	(	PUNCT
ma-51	159	14	1−	1−	NUM
ma-51	159	15	δn)(1−	δn)(1−	PROPN
ma-51	159	16	γn)‖xn	γn)‖xn	PROPN
ma-51	159	17	−	−	NOUN
ma-51	159	18	αq‖2	αq‖2	NOUN
ma-51	159	19	+	+	CCONJ
ma-51	159	20	(	(	PUNCT
ma-51	159	21	1−	1−	NUM
ma-51	159	22	δn)γn‖tyn	δn)γn‖tyn	NOUN
ma-51	159	23	−	−	PROPN
ma-51	159	24	αq‖2	αq‖2	PROPN
ma-51	159	25	−	−	PROPN
ma-51	159	26	γn(1−	γn(1−	NOUN
ma-51	159	27	γn)(1−	γn)(1−	PROPN
ma-51	159	28	δn)‖xn	δn)‖xn	NOUN
ma-51	159	29	−	−	NOUN
ma-51	159	30	tyn‖2	tyn‖2	PUNCT
ma-51	160	1	+	+	ADJ
ma-51	160	2	δnγ	δnγ	NOUN
ma-51	160	3	2	2	NUM
ma-51	160	4	n‖tyn	n‖tyn	ADV
ma-51	160	5	−	−	PROPN
ma-51	160	6	xn‖2	xn‖2	PROPN
ma-51	160	7	−	−	PROPN
ma-51	161	1	δn(1−	δn(1−	PROPN
ma-51	161	2	δn)‖xn	δn)‖xn	NOUN
ma-51	161	3	−	−	PROPN
ma-51	161	4	αq‖2	αq‖2	PROPN
ma-51	161	5	≤	≤	NUM
ma-51	161	6	(	(	PUNCT
ma-51	161	7	1−	1−	NUM
ma-51	161	8	δn)(1−	δn)(1−	PROPN
ma-51	161	9	γn)‖xn	γn)‖xn	PROPN
ma-51	161	10	−	−	NOUN
ma-51	161	11	αq‖2	αq‖2	NOUN
ma-51	161	12	+	+	CCONJ
ma-51	161	13	(	(	PUNCT
ma-51	161	14	1−	1−	NUM
ma-51	161	15	δn)γnl	δn)γnl	ADP
ma-51	161	16	2‖yn	2‖yn	NOUN
ma-51	161	17	−	−	PROPN
ma-51	161	18	αq‖2	αq‖2	PROPN
ma-51	161	19	−(γn	−(γn	NOUN
ma-51	161	20	−	−	NOUN
ma-51	161	21	δnγn	δnγn	NOUN
ma-51	161	22	−	−	NOUN
ma-51	161	23	γ2n	γ2n	X
ma-51	161	24	+	+	CCONJ
ma-51	161	25	γ2nδn)‖xn	γ2nδn)‖xn	PROPN
ma-51	161	26	−	−	PROPN
ma-51	161	27	tyn‖2	tyn‖2	NOUN
ma-51	162	1	+	+	NUM
ma-51	162	2	δnγ	δnγ	NOUN
ma-51	162	3	2	2	NUM
ma-51	162	4	n‖tyn	n‖tyn	ADV
ma-51	162	5	−	−	PROPN
ma-51	162	6	xn‖2	xn‖2	PROPN
ma-51	162	7	−	−	PROPN
ma-51	162	8	δn(1−	δn(1−	PROPN
ma-51	162	9	δn)‖xn	δn)‖xn	NOUN
ma-51	162	10	−	−	NOUN
ma-51	162	11	αq‖2	αq‖2	NOUN
ma-51	162	12	=	=	PUNCT
ma-51	162	13	(	(	PUNCT
ma-51	162	14	1−	1−	NUM
ma-51	162	15	δn)(1−	δn)(1−	PROPN
ma-51	162	16	γn)‖xn	γn)‖xn	PROPN
ma-51	162	17	−	−	NOUN
ma-51	162	18	αq‖2	αq‖2	NOUN
ma-51	162	19	+	+	CCONJ
ma-51	162	20	γnl	γnl	NOUN
ma-51	162	21	2‖yn	2‖yn	NOUN
ma-51	162	22	−	−	PROPN
ma-51	163	1	αq‖2	αq‖2	PROPN
ma-51	163	2	−	−	PROPN
ma-51	163	3	δnγnl2‖yn	δnγnl2‖yn	NOUN
ma-51	163	4	−	−	PROPN
ma-51	163	5	αq‖2	αq‖2	PROPN
ma-51	163	6	−(γn	−(γn	NOUN
ma-51	163	7	−	−	PRON
ma-51	163	8	δnγn	δnγn	NOUN
ma-51	163	9	−	−	PROPN
ma-51	163	10	γ2n)‖xn	γ2n)‖xn	PROPN
ma-51	163	11	−	−	PROPN
ma-51	163	12	tyn‖2	tyn‖2	NOUN
ma-51	164	1	−	−	PROPN
ma-51	164	2	δn(1−	δn(1−	PROPN
ma-51	164	3	δn)‖xn	δn)‖xn	NOUN
ma-51	164	4	−	−	NOUN
ma-51	164	5	αq‖2	αq‖2	PROPN
ma-51	164	6	.	.	PUNCT
ma-51	165	1	(	(	PUNCT
ma-51	165	2	3.9	3.9	NUM
ma-51	165	3	)	)	PUNCT
ma-51	165	4	observr	observr	NOUN
ma-51	165	5	that	that	SCONJ
ma-51	165	6	|xn	|xn	PRON
ma-51	165	7	−	−	NUM
ma-51	165	8	tyn‖	tyn‖	NOUN
ma-51	165	9	≤	≤	NOUN
ma-51	165	10	(	(	PUNCT
ma-51	165	11	‖xn	‖xn	PROPN
ma-51	165	12	−	−	NOUN
ma-51	165	13	αq‖+	αq‖+	PROPN
ma-51	166	1	l‖yn	l‖yn	PROPN
ma-51	166	2	−	−	PROPN
ma-51	166	3	αq‖)2	αq‖)2	PRON
ma-51	167	1	=	=	SYM
ma-51	167	2	‖xn	‖xn	NUM
ma-51	167	3	−	−	NOUN
ma-51	167	4	αq‖2	αq‖2	PROPN
ma-51	167	5	+	+	CCONJ
ma-51	167	6	l(2‖xn	l(2‖xn	PROPN
ma-51	167	7	−	−	PROPN
ma-51	167	8	αq‖‖yn	αq‖‖yn	NOUN
ma-51	167	9	−	−	NOUN
ma-51	167	10	αq‖	αq‖	NOUN
ma-51	167	11	)	)	PUNCT
ma-51	168	1	+	+	CCONJ
ma-51	168	2	l2‖yn	l2‖yn	ADJ
ma-51	168	3	−	−	PROPN
ma-51	168	4	αq‖2	αq‖2	PROPN
ma-51	168	5	≤	≤	PUNCT
ma-51	169	1	‖xn	‖xn	PUNCT
ma-51	169	2	−	−	NOUN
ma-51	169	3	αq‖2	αq‖2	NOUN
ma-51	169	4	+	+	CCONJ
ma-51	169	5	l‖xn	l‖xn	PROPN
ma-51	169	6	−	−	PROPN
ma-51	169	7	αq‖2	αq‖2	PROPN
ma-51	170	1	+	+	CCONJ
ma-51	170	2	l‖yn	l‖yn	AUX
ma-51	170	3	−	−	PROPN
ma-51	170	4	αq‖2	αq‖2	NOUN
ma-51	170	5	+	+	CCONJ
ma-51	170	6	l2‖yn	l2‖yn	ADJ
ma-51	170	7	−	−	PROPN
ma-51	170	8	αq‖2	αq‖2	PROPN
ma-51	170	9	=	=	PUNCT
ma-51	170	10	(	(	PUNCT
ma-51	170	11	1	1	NUM
ma-51	170	12	+	+	CCONJ
ma-51	170	13	l)‖xn	l)‖xn	X
ma-51	170	14	−	−	NOUN
ma-51	170	15	αq‖2	αq‖2	PROPN
ma-51	170	16	+	+	CCONJ
ma-51	170	17	l(1	l(1	PROPN
ma-51	170	18	+	+	CCONJ
ma-51	170	19	l)‖yn	l)‖yn	NOUN
ma-51	170	20	−	−	NOUN
ma-51	170	21	αq‖2	αq‖2	PROPN
ma-51	170	22	.	.	PUNCT
ma-51	171	1	(	(	PUNCT
ma-51	171	2	3.10	3.10	NUM
ma-51	171	3	)	)	PUNCT
ma-51	171	4	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	171	5	eur	eur	PROPN
ma-51	171	6	.	.	PUNCT
ma-51	172	1	j.	j.	PROPN
ma-51	172	2	math	math	PROPN
ma-51	172	3	.	.	PUNCT
ma-51	173	1	anal	anal	PROPN
ma-51	173	2	.	.	PUNCT
ma-51	174	1	10.28924	10.28924	NUM
ma-51	174	2	/	/	SYM
ma-51	174	3	ada	ada	PROPN
ma-51	174	4	/	/	SYM
ma-51	174	5	ma.2.10	ma.2.10	PROPN
ma-51	174	6	7(3.9	7(3.9	NUM
ma-51	174	7	)	)	PUNCT
ma-51	174	8	and	and	CCONJ
ma-51	174	9	(	(	PUNCT
ma-51	174	10	3.10	3.10	NUM
ma-51	174	11	)	)	PUNCT
ma-51	174	12	imply	imply	VERB
ma-51	174	13	qn	qn	NOUN
ma-51	174	14	≤	≤	NOUN
ma-51	175	1	(	(	PUNCT
ma-51	175	2	1−	1−	NUM
ma-51	175	3	δn)(1−	δn)(1−	PROPN
ma-51	175	4	γn)‖xn	γn)‖xn	PROPN
ma-51	175	5	−	−	NOUN
ma-51	176	1	αq‖2	αq‖2	NOUN
ma-51	176	2	+	+	CCONJ
ma-51	176	3	γnl	γnl	NOUN
ma-51	176	4	2‖yn	2‖yn	NOUN
ma-51	176	5	−	−	PROPN
ma-51	177	1	αq‖2	αq‖2	PROPN
ma-51	177	2	−	−	PROPN
ma-51	177	3	δnγnl2‖yn	δnγnl2‖yn	NOUN
ma-51	177	4	−	−	PROPN
ma-51	177	5	αq‖2	αq‖2	PROPN
ma-51	177	6	−(γn	−(γn	NOUN
ma-51	177	7	−	−	NOUN
ma-51	177	8	δnγn	δnγn	NOUN
ma-51	177	9	−	−	PROPN
ma-51	177	10	γ2n)[(1	γ2n)[(1	NOUN
ma-51	177	11	+	+	X
ma-51	177	12	l)‖xn	l)‖xn	X
ma-51	177	13	−	−	NOUN
ma-51	177	14	αq‖2	αq‖2	PROPN
ma-51	177	15	+	+	CCONJ
ma-51	177	16	l(1	l(1	PROPN
ma-51	177	17	+	+	CCONJ
ma-51	177	18	l)‖yn	l)‖yn	NOUN
ma-51	177	19	−	−	NOUN
ma-51	177	20	αq‖2]−	αq‖2]−	ADJ
ma-51	177	21	δn(1−	δn(1−	PROPN
ma-51	177	22	δn)‖xn	δn)‖xn	NOUN
ma-51	177	23	−	−	NOUN
ma-51	177	24	αq‖2	αq‖2	NOUN
ma-51	177	25	=	=	PUNCT
ma-51	177	26	(	(	PUNCT
ma-51	177	27	1−	1−	NUM
ma-51	177	28	δn)(1−	δn)(1−	PROPN
ma-51	177	29	γn)‖xn	γn)‖xn	PROPN
ma-51	177	30	−	−	PROPN
ma-51	177	31	αq‖2	αq‖2	PROPN
ma-51	177	32	−	−	PROPN
ma-51	177	33	(	(	PUNCT
ma-51	177	34	1	1	NUM
ma-51	177	35	+	+	CCONJ
ma-51	177	36	l)(γn	l)(γn	VERB
ma-51	177	37	−	−	PROPN
ma-51	177	38	δnγn	δnγn	NOUN
ma-51	177	39	−	−	PROPN
ma-51	177	40	γ2n)‖xn	γ2n)‖xn	PROPN
ma-51	177	41	−	−	PROPN
ma-51	177	42	αq‖	αq‖	NOUN
ma-51	177	43	−[(γn	−[(γn	PROPN
ma-51	177	44	−	−	PROPN
ma-51	177	45	δnγn	δnγn	NOUN
ma-51	177	46	−	−	PROPN
ma-51	177	47	γ2n)l−	γ2n)l−	ADP
ma-51	177	48	l2γ2n	l2γ2n	PUNCT
ma-51	177	49	]	]	PUNCT
ma-51	177	50	‖yn	‖yn	NUM
ma-51	177	51	−	−	NOUN
ma-51	177	52	αq‖2	αq‖2	PROPN
ma-51	177	53	−	−	PROPN
ma-51	177	54	δn(1−	δn(1−	PROPN
ma-51	177	55	δn)‖xn	δn)‖xn	NOUN
ma-51	177	56	−	−	NOUN
ma-51	177	57	αq‖2	αq‖2	PROPN
ma-51	177	58	(	(	PUNCT
ma-51	177	59	3.11	3.11	NUM
ma-51	177	60	)	)	PUNCT
ma-51	177	61	again	again	ADV
ma-51	177	62	,	,	PUNCT
ma-51	177	63	from	from	ADP
ma-51	177	64	(	(	PUNCT
ma-51	177	65	3.1	3.1	NUM
ma-51	177	66	)	)	PUNCT
ma-51	177	67	,	,	PUNCT
ma-51	177	68	we	we	PRON
ma-51	177	69	get	get	VERB
ma-51	177	70	‖yn	‖yn	PROPN
ma-51	177	71	−	−	NOUN
ma-51	177	72	αq‖2	αq‖2	PROPN
ma-51	177	73	=	=	SYM
ma-51	177	74	‖(1−	‖(1−	PROPN
ma-51	177	75	βn)(xn	βn)(xn	X
ma-51	177	76	−	−	PROPN
ma-51	177	77	αq	αq	X
ma-51	177	78	)	)	PUNCT
ma-51	178	1	+	+	CCONJ
ma-51	178	2	βn(txn	βn(txn	ADJ
ma-51	178	3	−	−	PROPN
ma-51	178	4	αq)‖2	αq)‖2	NOUN
ma-51	178	5	(	(	PUNCT
ma-51	178	6	3.12	3.12	NUM
ma-51	178	7	)	)	PUNCT
ma-51	178	8	since	since	SCONJ
ma-51	178	9	t	t	PROPN
ma-51	178	10	is	be	AUX
ma-51	178	11	α	α	DET
ma-51	178	12	-	-	ADJ
ma-51	178	13	hemicontractive	hemicontractive	ADJ
ma-51	178	14	mapping	mapping	NOUN
ma-51	178	15	,	,	PUNCT
ma-51	178	16	it	it	PRON
ma-51	178	17	follows	follow	VERB
ma-51	178	18	from	from	ADP
ma-51	178	19	(	(	PUNCT
ma-51	178	20	3.12	3.12	NUM
ma-51	178	21	)	)	PUNCT
ma-51	178	22	and	and	CCONJ
ma-51	178	23	lemma	lemma	PROPN
ma-51	178	24	2.1	2.1	NUM
ma-51	178	25	that	that	DET
ma-51	178	26	‖yn	‖yn	NUM
ma-51	178	27	−	−	NOUN
ma-51	178	28	αq‖2	αq‖2	PROPN
ma-51	178	29	≤	≤	NUM
ma-51	178	30	(	(	PUNCT
ma-51	178	31	1−	1−	NUM
ma-51	178	32	βn)‖xn	βn)‖xn	PRON
ma-51	178	33	−	−	PUNCT
ma-51	179	1	αq‖2	αq‖2	PROPN
ma-51	179	2	+	+	CCONJ
ma-51	179	3	βn[‖xn	βn[‖xn	PROPN
ma-51	179	4	−	−	PROPN
ma-51	179	5	αq‖2‖2	αq‖2‖2	PROPN
ma-51	180	1	+	+	CCONJ
ma-51	180	2	‖xn	‖xn	PROPN
ma-51	180	3	−	−	NOUN
ma-51	180	4	txn‖2]−	txn‖2]−	NOUN
ma-51	180	5	βn(1−	βn(1−	PROPN
ma-51	180	6	βn)‖xn	βn)‖xn	PRON
ma-51	180	7	−	−	NOUN
ma-51	180	8	txn‖2	txn‖2	NOUN
ma-51	181	1	=	=	SYM
ma-51	181	2	(	(	PUNCT
ma-51	181	3	1−	1−	NUM
ma-51	181	4	βn)‖xn	βn)‖xn	PRON
ma-51	181	5	−	−	PUNCT
ma-51	182	1	αq‖2	αq‖2	PROPN
ma-51	182	2	+	+	CCONJ
ma-51	182	3	β2n‖xn	β2n‖xn	PROPN
ma-51	182	4	−	−	PROPN
ma-51	182	5	txn‖2	txn‖2	NOUN
ma-51	182	6	.	.	PUNCT
ma-51	183	1	(	(	PUNCT
ma-51	183	2	3.13	3.13	NUM
ma-51	183	3	)	)	PUNCT
ma-51	183	4	putting	put	VERB
ma-51	183	5	(	(	PUNCT
ma-51	183	6	3.13	3.13	NUM
ma-51	183	7	)	)	PUNCT
ma-51	183	8	into	into	ADP
ma-51	183	9	(	(	PUNCT
ma-51	183	10	3.11	3.11	NUM
ma-51	183	11	)	)	PUNCT
ma-51	183	12	,	,	PUNCT
ma-51	183	13	we	we	PRON
ma-51	183	14	have	have	VERB
ma-51	183	15	qn	qn	PRON
ma-51	183	16	≤	≤	NOUN
ma-51	183	17	(	(	PUNCT
ma-51	183	18	1−	1−	NUM
ma-51	183	19	δn)(1−	δn)(1−	PROPN
ma-51	183	20	γn)‖xn	γn)‖xn	PROPN
ma-51	183	21	−	−	PROPN
ma-51	183	22	αq‖2	αq‖2	PROPN
ma-51	183	23	−	−	PROPN
ma-51	183	24	(	(	PUNCT
ma-51	183	25	1	1	NUM
ma-51	183	26	+	+	CCONJ
ma-51	183	27	l)(γn	l)(γn	VERB
ma-51	183	28	−	−	PROPN
ma-51	183	29	δnγn	δnγn	NOUN
ma-51	183	30	−	−	PROPN
ma-51	183	31	γ2n)‖xn	γ2n)‖xn	PROPN
ma-51	183	32	−	−	PROPN
ma-51	183	33	αq‖	αq‖	NOUN
ma-51	183	34	−[(γn	−[(γn	PROPN
ma-51	183	35	−	−	PROPN
ma-51	183	36	δnγn	δnγn	NOUN
ma-51	183	37	−	−	PROPN
ma-51	183	38	γ2n)l−	γ2n)l−	ADP
ma-51	183	39	l2γ2n	l2γ2n	PUNCT
ma-51	183	40	]	]	X
ma-51	183	41	{	{	PUNCT
ma-51	183	42	(	(	PUNCT
ma-51	183	43	1−	1−	NUM
ma-51	183	44	βn)‖xn	βn)‖xn	PRON
ma-51	183	45	−	−	PUNCT
ma-51	184	1	αq‖2	αq‖2	PROPN
ma-51	184	2	+	+	CCONJ
ma-51	184	3	β2n‖xn	β2n‖xn	PROPN
ma-51	184	4	−	−	PROPN
ma-51	184	5	txn‖2	txn‖2	NOUN
ma-51	184	6	}	}	PUNCT
ma-51	184	7	−δn(1−	−δn(1−	PROPN
ma-51	184	8	δn)‖xn	δn)‖xn	PROPN
ma-51	184	9	−	−	PROPN
ma-51	184	10	αq‖2	αq‖2	PROPN
ma-51	184	11	≤	≤	NUM
ma-51	184	12	(	(	PUNCT
ma-51	184	13	1−	1−	NUM
ma-51	184	14	δn)(1−	δn)(1−	PROPN
ma-51	184	15	γn)‖xn	γn)‖xn	PROPN
ma-51	184	16	−	−	PROPN
ma-51	184	17	αq‖2	αq‖2	NOUN
ma-51	184	18	−	−	PROPN
ma-51	185	1	[	[	X
ma-51	185	2	(	(	PUNCT
ma-51	185	3	γn	γn	NOUN
ma-51	185	4	−	−	PROPN
ma-51	185	5	δnγn	δnγn	NOUN
ma-51	185	6	−	−	NOUN
ma-51	185	7	γ2n)(1	γ2n)(1	X
ma-51	185	8	+	+	X
ma-51	185	9	l	l	NOUN
ma-51	185	10	)	)	PUNCT
ma-51	186	1	+	+	CCONJ
ma-51	186	2	δn(1−	δn(1−	ADJ
ma-51	186	3	δn)−	δn)−	NOUN
ma-51	186	4	l2γ2n	l2γ2n	PUNCT
ma-51	186	5	]	]	X
ma-51	186	6	‖xn	‖xn	NUM
ma-51	186	7	−	−	PROPN
ma-51	186	8	αq‖2	αq‖2	NOUN
ma-51	186	9	−β2n	−β2n	PUNCT
ma-51	187	1	[	[	X
ma-51	187	2	(	(	PUNCT
ma-51	187	3	γn	γn	NOUN
ma-51	187	4	−	−	NOUN
ma-51	187	5	δnγn	δnγn	NOUN
ma-51	187	6	−	−	PROPN
ma-51	187	7	γ2n)l−	γ2n)l−	ADP
ma-51	187	8	l2γ2n	l2γ2n	PUNCT
ma-51	187	9	]	]	X
ma-51	187	10	‖xn	‖xn	PROPN
ma-51	187	11	−	−	PROPN
ma-51	187	12	txn‖2	txn‖2	NOUN
ma-51	187	13	.	.	PUNCT
ma-51	188	1	(	(	PUNCT
ma-51	188	2	3.14	3.14	NUM
ma-51	188	3	)	)	PUNCT
ma-51	188	4	since	since	SCONJ
ma-51	188	5	from	from	ADP
ma-51	188	6	condition	condition	NOUN
ma-51	188	7	(	(	PUNCT
ma-51	188	8	i	i	NOUN
ma-51	188	9	)	)	PUNCT
ma-51	188	10	,	,	PUNCT
ma-51	188	11	(	(	PUNCT
ma-51	188	12	γn	γn	NOUN
ma-51	188	13	−	−	NOUN
ma-51	188	14	δnγn	δnγn	NOUN
ma-51	188	15	−	−	PROPN
ma-51	188	16	γ2n)−	γ2n)−	NOUN
ma-51	188	17	l2γ2n	l2γ2n	PUNCT
ma-51	188	18	≥	≥	NOUN
ma-51	188	19	0	0	NUM
ma-51	188	20	,	,	PUNCT
ma-51	188	21	it	it	PRON
ma-51	188	22	follows	follow	VERB
ma-51	188	23	from	from	ADP
ma-51	188	24	(	(	PUNCT
ma-51	188	25	3.14	3.14	NUM
ma-51	188	26	)	)	PUNCT
ma-51	189	1	that	that	PRON
ma-51	189	2	qn	qn	VERB
ma-51	189	3	≤	≤	X
ma-51	189	4	(	(	PUNCT
ma-51	189	5	1−	1−	NUM
ma-51	189	6	δn)2‖xn	δn)2‖xn	PROPN
ma-51	189	7	−	−	PROPN
ma-51	189	8	αq‖2	αq‖2	PROPN
ma-51	189	9	(	(	PUNCT
ma-51	189	10	3.15	3.15	NUM
ma-51	189	11	)	)	PUNCT
ma-51	189	12	(	(	PUNCT
ma-51	189	13	3.2	3.2	NUM
ma-51	189	14	)	)	PUNCT
ma-51	189	15	and	and	CCONJ
ma-51	189	16	(	(	PUNCT
ma-51	189	17	3.15	3.15	NUM
ma-51	189	18	)	)	PUNCT
ma-51	189	19	imply	imply	VERB
ma-51	189	20	|xn+1	|xn+1	NOUN
ma-51	189	21	−	−	NOUN
ma-51	189	22	αq‖	αq‖	NOUN
ma-51	189	23	≤	≤	NOUN
ma-51	189	24	(	(	PUNCT
ma-51	189	25	1−	1−	NUM
ma-51	189	26	δn)‖xn	δn)‖xn	PROPN
ma-51	189	27	−	−	PROPN
ma-51	189	28	αq‖2	αq‖2	PROPN
ma-51	189	29	+	+	CCONJ
ma-51	189	30	δn‖αq‖	δn‖αq‖	ADJ
ma-51	189	31	≤	≤	ADJ
ma-51	189	32	max{‖xn	max{‖xn	NOUN
ma-51	189	33	−	−	PROPN
ma-51	189	34	αq‖2	αq‖2	PROPN
ma-51	189	35	,	,	PUNCT
ma-51	189	36	‖αq‖},∀n	‖αq‖},∀n	NOUN
ma-51	190	1	∈	∈	PROPN
ma-51	190	2	n.	n.	NOUN
ma-51	190	3	it	it	PRON
ma-51	190	4	is	be	AUX
ma-51	190	5	easy	easy	ADJ
ma-51	190	6	to	to	PART
ma-51	190	7	see	see	VERB
ma-51	190	8	,	,	PUNCT
ma-51	190	9	using	use	VERB
ma-51	190	10	mathematical	mathematical	ADJ
ma-51	190	11	induction	induction	NOUN
ma-51	190	12	,	,	PUNCT
ma-51	190	13	that	that	PRON
ma-51	190	14	|xn+1	|xn+1	VERB
ma-51	190	15	−	−	NOUN
ma-51	190	16	αq‖	αq‖	NOUN
ma-51	190	17	≤	≤	NOUN
ma-51	190	18	max{‖xn	max{‖xn	NOUN
ma-51	190	19	−	−	PROPN
ma-51	190	20	αq‖2	αq‖2	PROPN
ma-51	190	21	,	,	PUNCT
ma-51	190	22	‖αq‖	‖αq‖	NOUN
ma-51	190	23	}	}	PUNCT
ma-51	190	24	=	=	SYM
ma-51	191	1	‖x0	‖x0	NUM
ma-51	192	1	−	−	PROPN
ma-51	192	2	αq‖2	αq‖2	PROPN
ma-51	192	3	.	.	PUNCT
ma-51	193	1	(	(	PUNCT
ma-51	193	2	3.16	3.16	NUM
ma-51	193	3	)	)	PUNCT
ma-51	193	4	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	193	5	eur	eur	PROPN
ma-51	193	6	.	.	PUNCT
ma-51	194	1	j.	j.	PROPN
ma-51	194	2	math	math	PROPN
ma-51	194	3	.	.	PUNCT
ma-51	195	1	anal	anal	PROPN
ma-51	195	2	.	.	PUNCT
ma-51	196	1	10.28924	10.28924	NUM
ma-51	196	2	/	/	SYM
ma-51	196	3	ada	ada	PROPN
ma-51	196	4	/	/	SYM
ma-51	196	5	ma.2.10	ma.2.10	PROPN
ma-51	196	6	8hence	8hence	NUM
ma-51	196	7	,	,	PUNCT
ma-51	196	8	{	{	PUNCT
ma-51	196	9	xn}∞n=0	xn}∞n=0	X
ma-51	196	10	is	be	AUX
ma-51	196	11	bounded.furthermore	bounded.furthermore	NOUN
ma-51	196	12	,	,	PUNCT
ma-51	196	13	since	since	SCONJ
ma-51	196	14	from	from	ADP
ma-51	196	15	(	(	PUNCT
ma-51	196	16	3.1	3.1	NUM
ma-51	196	17	)	)	PUNCT
ma-51	196	18	,	,	PUNCT
ma-51	196	19	‖xn+1	‖xn+1	NUM
ma-51	197	1	−	−	NOUN
ma-51	197	2	αq‖2	αq‖2	PROPN
ma-51	197	3	=	=	PUNCT
ma-51	197	4	‖pk[(1−	‖pk[(1−	NOUN
ma-51	197	5	δn	δn	ADP
ma-51	197	6	−	−	X
ma-51	197	7	γn)xn	γn)xn	PROPN
ma-51	197	8	+	+	CCONJ
ma-51	197	9	γntyn]−	γntyn]−	PROPN
ma-51	197	10	αq‖2	αq‖2	NOUN
ma-51	197	11	≤	≤	NUM
ma-51	197	12	‖(1−	‖(1−	PROPN
ma-51	197	13	δn	δn	NOUN
ma-51	197	14	−	−	X
ma-51	197	15	γn)xn	γn)xn	PROPN
ma-51	197	16	+	+	CCONJ
ma-51	197	17	γntyn	γntyn	NOUN
ma-51	197	18	−	−	PROPN
ma-51	198	1	αq‖2	αq‖2	PROPN
ma-51	198	2	=	=	PUNCT
ma-51	199	1	‖xn	‖xn	PROPN
ma-51	199	2	−	−	PROPN
ma-51	199	3	αq	αq	ADP
ma-51	199	4	−	−	PROPN
ma-51	199	5	γn(xn	γn(xn	NOUN
ma-51	200	1	−	−	PROPN
ma-51	200	2	tyn)−	tyn)−	NOUN
ma-51	200	3	δnxn‖2	δnxn‖2	NOUN
ma-51	200	4	,	,	PUNCT
ma-51	200	5	it	it	PRON
ma-51	200	6	follows	follow	VERB
ma-51	200	7	from	from	ADP
ma-51	200	8	lemma	lemma	PROPN
ma-51	200	9	2.3(i	2.3(i	PROPN
ma-51	200	10	)	)	PUNCT
ma-51	201	1	that	that	SCONJ
ma-51	201	2	‖xn+1	‖xn+1	NUM
ma-51	201	3	−	−	NOUN
ma-51	202	1	αq‖2	αq‖2	PROPN
ma-51	202	2	≤	≤	PUNCT
ma-51	203	1	‖xn	‖xn	PUNCT
ma-51	203	2	−	−	PROPN
ma-51	203	3	αq	αq	ADP
ma-51	203	4	−	−	PROPN
ma-51	203	5	γn(xn	γn(xn	NOUN
ma-51	204	1	−	−	PROPN
ma-51	204	2	tyn)‖2	tyn)‖2	NOUN
ma-51	204	3	−	−	PROPN
ma-51	204	4	2δn〈xn	2δn〈xn	NUM
ma-51	204	5	,	,	PUNCT
ma-51	204	6	xn+1	xn+1	PROPN
ma-51	204	7	−	−	PROPN
ma-51	204	8	αq	αq	PROPN
ma-51	204	9	〉	〉	PROPN
ma-51	204	10	.	.	PUNCT
ma-51	205	1	(	(	PUNCT
ma-51	205	2	3.17	3.17	NUM
ma-51	205	3	)	)	PUNCT
ma-51	205	4	since	since	SCONJ
ma-51	205	5	‖xn	‖xn	PROPN
ma-51	205	6	−	−	PROPN
ma-51	205	7	αq	αq	ADP
ma-51	205	8	−	−	PROPN
ma-51	205	9	γn(xn	γn(xn	X
ma-51	206	1	−	−	NOUN
ma-51	206	2	tyn)‖2	tyn)‖2	NOUN
ma-51	206	3	=	=	SYM
ma-51	206	4	‖(1−	‖(1−	PROPN
ma-51	206	5	γn)(xn	γn)(xn	PUNCT
ma-51	206	6	−	−	PROPN
ma-51	206	7	αq	αq	NUM
ma-51	206	8	)	)	PUNCT
ma-51	207	1	+	+	CCONJ
ma-51	207	2	γn(αq	γn(αq	ADJ
ma-51	207	3	−	−	NOUN
ma-51	207	4	tyn)‖2	tyn)‖2	NOUN
ma-51	207	5	=	=	SYM
ma-51	207	6	(	(	PUNCT
ma-51	207	7	1−	1−	NUM
ma-51	207	8	γn)‖xn	γn)‖xn	NOUN
ma-51	207	9	−	−	NOUN
ma-51	207	10	αq‖2	αq‖2	NOUN
ma-51	207	11	+	+	CCONJ
ma-51	207	12	γn‖αq	γn‖αq	NOUN
ma-51	207	13	−	−	PROPN
ma-51	207	14	tyn‖2	tyn‖2	NOUN
ma-51	207	15	−	−	PROPN
ma-51	208	1	γn(1−	γn(1−	NUM
ma-51	208	2	γn)‖tyn	γn)‖tyn	ADP
ma-51	208	3	−	−	PUNCT
ma-51	208	4	xn‖2	xn‖2	PROPN
ma-51	208	5	≤	≤	PROPN
ma-51	208	6	(	(	PUNCT
ma-51	208	7	1−	1−	NUM
ma-51	208	8	γn)‖xn	γn)‖xn	NOUN
ma-51	208	9	−	−	NOUN
ma-51	209	1	αq‖2	αq‖2	NOUN
ma-51	209	2	+	+	CCONJ
ma-51	209	3	γnl	γnl	NOUN
ma-51	209	4	2‖yn	2‖yn	NOUN
ma-51	209	5	−	−	PROPN
ma-51	210	1	αq‖2	αq‖2	NOUN
ma-51	210	2	−γn(1−	−γn(1−	VERB
ma-51	210	3	γn)‖tyn	γn)‖tyn	ADP
ma-51	210	4	−	−	PROPN
ma-51	210	5	xn‖2	xn‖2	PROPN
ma-51	210	6	,	,	PUNCT
ma-51	210	7	(	(	PUNCT
ma-51	210	8	3.18	3.18	NUM
ma-51	210	9	)	)	PUNCT
ma-51	210	10	it	it	PRON
ma-51	210	11	follows	follow	VERB
ma-51	210	12	from	from	ADP
ma-51	210	13	(	(	PUNCT
ma-51	210	14	3.10	3.10	NUM
ma-51	210	15	)	)	PUNCT
ma-51	211	1	that	that	PRON
ma-51	211	2	‖xn	‖xn	PROPN
ma-51	211	3	−	−	PROPN
ma-51	211	4	αq	αq	ADP
ma-51	211	5	−	−	PROPN
ma-51	211	6	γn(xn	γn(xn	X
ma-51	211	7	−	−	NOUN
ma-51	211	8	tyn)‖2	tyn)‖2	NOUN
ma-51	211	9	≤	≤	NOUN
ma-51	211	10	(	(	PUNCT
ma-51	211	11	1−	1−	NUM
ma-51	211	12	γn)‖xn	γn)‖xn	NOUN
ma-51	211	13	−	−	NOUN
ma-51	211	14	αq‖2	αq‖2	NOUN
ma-51	211	15	+	+	CCONJ
ma-51	211	16	γnl	γnl	NOUN
ma-51	211	17	2‖yn	2‖yn	NOUN
ma-51	211	18	−	−	PROPN
ma-51	212	1	αq‖2	αq‖2	PROPN
ma-51	212	2	−γn(1−	−γn(1−	PUNCT
ma-51	212	3	γn){(1	γn){(1	PROPN
ma-51	212	4	+	+	CCONJ
ma-51	212	5	l)‖xn	l)‖xn	X
ma-51	212	6	−	−	NOUN
ma-51	212	7	αq‖2	αq‖2	PROPN
ma-51	212	8	+	+	CCONJ
ma-51	212	9	l(1	l(1	PROPN
ma-51	212	10	+	+	CCONJ
ma-51	212	11	l)‖yn	l)‖yn	NOUN
ma-51	212	12	−	−	NOUN
ma-51	213	1	αq‖2	αq‖2	PROPN
ma-51	213	2	}	}	PUNCT
ma-51	213	3	=	=	SYM
ma-51	213	4	(	(	PUNCT
ma-51	213	5	1−	1−	NUM
ma-51	213	6	γn)‖xn	γn)‖xn	NOUN
ma-51	213	7	−	−	NOUN
ma-51	214	1	αq‖2	αq‖2	NOUN
ma-51	214	2	+	+	CCONJ
ma-51	214	3	γnl	γnl	NOUN
ma-51	214	4	2‖yn	2‖yn	NOUN
ma-51	214	5	−	−	PROPN
ma-51	215	1	αq‖2	αq‖2	PROPN
ma-51	215	2	−γn(1−	−γn(1−	NOUN
ma-51	215	3	γn)(1	γn)(1	ADP
ma-51	215	4	+	+	X
ma-51	215	5	l)‖xn	l)‖xn	X
ma-51	215	6	−	−	PROPN
ma-51	215	7	αq‖2	αq‖2	PROPN
ma-51	215	8	−	−	PROPN
ma-51	215	9	γn(1−	γn(1−	NUM
ma-51	215	10	γn)l‖yn	γn)l‖yn	NOUN
ma-51	215	11	−	−	PROPN
ma-51	215	12	αq‖2	αq‖2	PROPN
ma-51	215	13	−γnl2‖yn	−γnl2‖yn	NOUN
ma-51	215	14	−	−	NOUN
ma-51	216	1	αq‖2	αq‖2	PROPN
ma-51	216	2	+	+	CCONJ
ma-51	216	3	γ2nl	γ2nl	NUM
ma-51	216	4	2‖yn	2‖yn	NOUN
ma-51	216	5	−	−	ADP
ma-51	216	6	αq‖2	αq‖2	PROPN
ma-51	216	7	=	=	SYM
ma-51	216	8	(	(	PUNCT
ma-51	216	9	1−	1−	NUM
ma-51	216	10	γn)‖xn	γn)‖xn	NOUN
ma-51	216	11	−	−	NOUN
ma-51	216	12	αq‖2	αq‖2	PROPN
ma-51	216	13	−	−	PROPN
ma-51	217	1	γn(1−	γn(1−	NUM
ma-51	217	2	γn)(1	γn)(1	ADP
ma-51	217	3	+	+	X
ma-51	217	4	l)‖xn	l)‖xn	X
ma-51	217	5	−	−	PROPN
ma-51	217	6	αq‖2	αq‖2	PROPN
ma-51	217	7	−[γn(1−	−[γn(1−	NOUN
ma-51	217	8	γn)l−	γn)l−	ADP
ma-51	217	9	l2γ2n	l2γ2n	PUNCT
ma-51	217	10	]	]	PUNCT
ma-51	217	11	‖yn	‖yn	NUM
ma-51	217	12	−	−	PROPN
ma-51	217	13	αq‖2	αq‖2	PROPN
ma-51	217	14	.	.	PUNCT
ma-51	218	1	(	(	PUNCT
ma-51	218	2	3.19	3.19	NUM
ma-51	218	3	)	)	PUNCT
ma-51	218	4	(	(	PUNCT
ma-51	218	5	3.13	3.13	NUM
ma-51	218	6	)	)	PUNCT
ma-51	218	7	and	and	CCONJ
ma-51	218	8	(	(	PUNCT
ma-51	218	9	3.19	3.19	NUM
ma-51	218	10	)	)	PUNCT
ma-51	218	11	imply	imply	VERB
ma-51	218	12	‖xn	‖xn	PROPN
ma-51	218	13	−	−	PROPN
ma-51	218	14	αq	αq	ADP
ma-51	218	15	−	−	PROPN
ma-51	218	16	γn(xn	γn(xn	X
ma-51	219	1	−	−	NOUN
ma-51	219	2	tyn)‖2	tyn)‖2	NOUN
ma-51	219	3	≤	≤	NOUN
ma-51	219	4	(	(	PUNCT
ma-51	219	5	1−	1−	NUM
ma-51	219	6	γn)‖xn	γn)‖xn	NOUN
ma-51	219	7	−	−	NOUN
ma-51	219	8	αq‖2	αq‖2	PROPN
ma-51	219	9	−	−	PROPN
ma-51	220	1	γn(1−	γn(1−	NUM
ma-51	220	2	γn)(1	γn)(1	ADP
ma-51	220	3	+	+	X
ma-51	220	4	l)‖xn	l)‖xn	X
ma-51	220	5	−	−	PROPN
ma-51	220	6	αq‖2	αq‖2	PROPN
ma-51	220	7	−[γn(1−	−[γn(1−	NOUN
ma-51	220	8	γn)l−	γn)l−	ADP
ma-51	220	9	l2γ2n	l2γ2n	PUNCT
ma-51	220	10	]	]	X
ma-51	220	11	{	{	PUNCT
ma-51	220	12	(	(	PUNCT
ma-51	220	13	1−	1−	NUM
ma-51	220	14	βn)‖xn	βn)‖xn	PRON
ma-51	220	15	−	−	PUNCT
ma-51	221	1	αq‖2	αq‖2	PROPN
ma-51	221	2	+	+	CCONJ
ma-51	221	3	β2n‖xn	β2n‖xn	PROPN
ma-51	221	4	−	−	PROPN
ma-51	221	5	txn‖2	txn‖2	NOUN
ma-51	221	6	}	}	PUNCT
ma-51	221	7	≤	≤	NOUN
ma-51	221	8	(	(	PUNCT
ma-51	221	9	1−	1−	NUM
ma-51	221	10	γn)‖xn	γn)‖xn	NOUN
ma-51	221	11	−	−	NOUN
ma-51	221	12	αq‖2	αq‖2	PROPN
ma-51	221	13	−	−	PROPN
ma-51	221	14	γnl[1−	γnl[1−	SYM
ma-51	221	15	γn	γn	ADP
ma-51	221	16	−	−	PROPN
ma-51	221	17	γnl]{(1−	γnl]{(1−	PUNCT
ma-51	221	18	βn)‖xn	βn)‖xn	PROPN
ma-51	221	19	−	−	PUNCT
ma-51	222	1	αq‖2	αq‖2	PROPN
ma-51	222	2	+	+	NOUN
ma-51	222	3	β2n‖xn	β2n‖xn	PROPN
ma-51	222	4	−	−	NOUN
ma-51	222	5	txn‖2	txn‖2	NOUN
ma-51	222	6	}	}	PUNCT
ma-51	222	7	.	.	PUNCT
ma-51	223	1	(	(	PUNCT
ma-51	223	2	3.20	3.20	NUM
ma-51	223	3	)	)	PUNCT
ma-51	223	4	by	by	ADP
ma-51	223	5	condition	condition	NOUN
ma-51	223	6	(	(	PUNCT
ma-51	223	7	i	i	NOUN
ma-51	223	8	)	)	PUNCT
ma-51	223	9	,	,	PUNCT
ma-51	223	10	1−	1−	NUM
ma-51	223	11	γn	γn	ADP
ma-51	223	12	−	−	PROPN
ma-51	223	13	γnl	γnl	PROPN
ma-51	223	14	>	>	X
ma-51	223	15	0,∀n	0,∀n	PROPN
ma-51	223	16	≥	≥	PROPN
ma-51	223	17	0	0	NUM
ma-51	223	18	.	.	PUNCT
ma-51	224	1	consequently	consequently	ADV
ma-51	224	2	,	,	PUNCT
ma-51	224	3	‖xn	‖xn	PROPN
ma-51	224	4	−	−	PROPN
ma-51	224	5	αq	αq	ADP
ma-51	224	6	−	−	PROPN
ma-51	224	7	γn(xn	γn(xn	X
ma-51	224	8	−	−	NOUN
ma-51	224	9	tyn)‖2	tyn)‖2	NOUN
ma-51	224	10	≤	≤	PUNCT
ma-51	225	1	‖xn	‖xn	NUM
ma-51	225	2	−	−	NOUN
ma-51	225	3	αq‖2	αq‖2	PROPN
ma-51	225	4	−(1−	−(1−	VERB
ma-51	225	5	γn	γn	ADP
ma-51	225	6	−	−	PROPN
ma-51	225	7	γnl)β2nγnl‖xn	γnl)β2nγnl‖xn	PROPN
ma-51	225	8	−	−	PROPN
ma-51	225	9	txn‖2	txn‖2	NOUN
ma-51	225	10	.	.	PUNCT
ma-51	226	1	(	(	PUNCT
ma-51	226	2	3.21	3.21	NUM
ma-51	226	3	)	)	PUNCT
ma-51	226	4	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	226	5	eur	eur	PROPN
ma-51	226	6	.	.	PUNCT
ma-51	227	1	j.	j.	PROPN
ma-51	227	2	math	math	PROPN
ma-51	227	3	.	.	PUNCT
ma-51	228	1	anal	anal	PROPN
ma-51	228	2	.	.	PUNCT
ma-51	229	1	10.28924	10.28924	NUM
ma-51	229	2	/	/	SYM
ma-51	229	3	ada	ada	PROPN
ma-51	229	4	/	/	SYM
ma-51	229	5	ma.2.10	ma.2.10	PROPN
ma-51	229	6	9(3.17)and	9(3.17)and	NUM
ma-51	229	7	(	(	PUNCT
ma-51	229	8	3.21	3.21	NUM
ma-51	229	9	)	)	PUNCT
ma-51	229	10	imply	imply	ADV
ma-51	229	11	‖xn+1	‖xn+1	NUM
ma-51	229	12	−	−	NOUN
ma-51	229	13	αq‖2	αq‖2	PROPN
ma-51	229	14	≤	≤	PUNCT
ma-51	230	1	‖xn	‖xn	PUNCT
ma-51	230	2	−	−	NOUN
ma-51	230	3	αq‖2	αq‖2	PROPN
ma-51	230	4	−	−	PROPN
ma-51	231	1	(	(	PUNCT
ma-51	231	2	1−	1−	NUM
ma-51	231	3	γn	γn	ADP
ma-51	231	4	−	−	PROPN
ma-51	231	5	γnl)β2nγnl‖xn	γnl)β2nγnl‖xn	PROPN
ma-51	231	6	−	−	PROPN
ma-51	232	1	txn‖2	txn‖2	NOUN
ma-51	233	1	−2δn〈xn	−2δn〈xn	PROPN
ma-51	233	2	,	,	PUNCT
ma-51	233	3	xn+1	xn+1	NUM
ma-51	233	4	−	−	PROPN
ma-51	233	5	αq	αq	PROPN
ma-51	233	6	〉	〉	PROPN
ma-51	233	7	.	.	PUNCT
ma-51	234	1	since	since	SCONJ
ma-51	234	2	{	{	PUNCT
ma-51	234	3	xn	xn	X
ma-51	234	4	}	}	PUNCT
ma-51	234	5	is	be	AUX
ma-51	234	6	bounded	bound	VERB
ma-51	234	7	,	,	PUNCT
ma-51	234	8	there	there	PRON
ma-51	234	9	exists	exist	VERB
ma-51	234	10	a	a	DET
ma-51	234	11	constant	constant	ADJ
ma-51	234	12	b	b	NOUN
ma-51	234	13	>	>	X
ma-51	234	14	0	0	NUM
ma-51	234	15	such	such	ADJ
ma-51	234	16	that	that	SCONJ
ma-51	234	17	−2〈xn	−2〈xn	ADV
ma-51	234	18	,	,	PUNCT
ma-51	234	19	xn+1	xn+1	VERB
ma-51	234	20	−	−	PROPN
ma-51	235	1	αq	αq	ADP
ma-51	235	2	〉	〉	PROPN
ma-51	235	3	≤	≤	PROPN
ma-51	235	4	b.	b.	PROPN
ma-51	235	5	thus	thus	ADV
ma-51	235	6	,	,	PUNCT
ma-51	235	7	‖xn+1	‖xn+1	NUM
ma-51	235	8	−	−	PROPN
ma-51	235	9	αq‖2	αq‖2	PROPN
ma-51	235	10	≤	≤	PUNCT
ma-51	236	1	‖xn	‖xn	PUNCT
ma-51	236	2	−	−	NOUN
ma-51	236	3	αq‖2	αq‖2	PROPN
ma-51	236	4	−	−	PROPN
ma-51	237	1	(	(	PUNCT
ma-51	237	2	1−	1−	NUM
ma-51	237	3	γn	γn	ADP
ma-51	237	4	−	−	PROPN
ma-51	237	5	γnl)β2nγnl‖xn	γnl)β2nγnl‖xn	PROPN
ma-51	237	6	−	−	PROPN
ma-51	237	7	txn‖2	txn‖2	NOUN
ma-51	237	8	δnb	δnb	PROPN
ma-51	237	9	.	.	PUNCT
ma-51	238	1	the	the	DET
ma-51	238	2	last	last	ADJ
ma-51	238	3	inequality	inequality	NOUN
ma-51	238	4	implies	imply	VERB
ma-51	238	5	that	that	SCONJ
ma-51	238	6	‖xn+1	‖xn+1	NUM
ma-51	238	7	−	−	PRON
ma-51	238	8	αq‖2	αq‖2	NOUN
ma-51	238	9	−	−	PROPN
ma-51	238	10	‖xn	‖xn	NUM
ma-51	238	11	−	−	PROPN
ma-51	238	12	αq‖2	αq‖2	NOUN
ma-51	238	13	+	+	CCONJ
ma-51	238	14	(	(	PUNCT
ma-51	238	15	1−	1−	NUM
ma-51	238	16	γn	γn	ADP
ma-51	238	17	−	−	PROPN
ma-51	238	18	γnl)β2nγnl‖xn	γnl)β2nγnl‖xn	PROPN
ma-51	238	19	−	−	PROPN
ma-51	238	20	txn‖2	txn‖2	NOUN
ma-51	238	21	≤	≤	NOUN
ma-51	238	22	δnb	δnb	NOUN
ma-51	238	23	.	.	PUNCT
ma-51	239	1	(	(	PUNCT
ma-51	239	2	3.22	3.22	NUM
ma-51	239	3	)	)	PUNCT
ma-51	239	4	now	now	ADV
ma-51	239	5	,	,	PUNCT
ma-51	239	6	we	we	PRON
ma-51	239	7	consider	consider	VERB
ma-51	239	8	the	the	DET
ma-51	239	9	following	follow	VERB
ma-51	239	10	two	two	NUM
ma-51	239	11	cases	case	NOUN
ma-51	239	12	:	:	PUNCT
ma-51	239	13	case	case	NOUN
ma-51	239	14	a	a	X
ma-51	239	15	:	:	PUNCT
ma-51	239	16	suppose	suppose	VERB
ma-51	239	17	there	there	PRON
ma-51	239	18	exists	exist	VERB
ma-51	239	19	n0	n0	PROPN
ma-51	239	20	∈	∈	PROPN
ma-51	239	21	n	n	PRON
ma-51	239	22	such	such	ADJ
ma-51	239	23	that	that	SCONJ
ma-51	239	24	{	{	PUNCT
ma-51	239	25	‖xn	‖xn	PROPN
ma-51	239	26	−αq‖	−αq‖	NOUN
ma-51	239	27	}	}	PUNCT
ma-51	239	28	is	be	AUX
ma-51	239	29	non	non	ADJ
ma-51	239	30	-	-	ADJ
ma-51	239	31	increasing	increase	VERB
ma-51	239	32	.	.	PUNCT
ma-51	240	1	then	then	ADV
ma-51	240	2	,	,	PUNCT
ma-51	240	3	{	{	PUNCT
ma-51	240	4	‖xn	‖xn	PROPN
ma-51	240	5	−αq‖}is	−αq‖}is	PROPN
ma-51	240	6	convergent	convergent	NOUN
ma-51	240	7	.	.	PUNCT
ma-51	241	1	clearly	clearly	ADV
ma-51	241	2	,	,	PUNCT
ma-51	241	3	‖xn+1−αq‖−‖xn−αq‖	‖xn+1−αq‖−‖xn−αq‖	NOUN
ma-51	241	4	→	→	SYM
ma-51	241	5	0	0	NUM
ma-51	241	6	.	.	PUNCT
ma-51	242	1	in	in	ADP
ma-51	242	2	view	view	NOUN
ma-51	242	3	,	,	PUNCT
ma-51	242	4	of	of	ADP
ma-51	242	5	condition	condition	NOUN
ma-51	242	6	(	(	PUNCT
ma-51	242	7	i	i	PRON
ma-51	242	8	i	i	PROPN
ma-51	242	9	)	)	PUNCT
ma-51	242	10	and	and	CCONJ
ma-51	242	11	(	(	PUNCT
ma-51	242	12	3.22	3.22	NUM
ma-51	242	13	)	)	PUNCT
ma-51	242	14	,	,	PUNCT
ma-51	242	15	we	we	PRON
ma-51	242	16	have	have	VERB
ma-51	242	17	‖xn−txn‖	‖xn−txn‖	NOUN
ma-51	242	18	→	→	SYM
ma-51	242	19	0	0	NUM
ma-51	242	20	.	.	PUNCT
ma-51	243	1	by	by	ADP
ma-51	243	2	lemma	lemma	PROPN
ma-51	243	3	2.4	2.4	NUM
ma-51	243	4	,	,	PUNCT
ma-51	243	5	it	it	PRON
ma-51	243	6	is	be	AUX
ma-51	243	7	obvious	obvious	ADJ
ma-51	243	8	that	that	SCONJ
ma-51	243	9	ωω(xn	ωω(xn	NUM
ma-51	243	10	)	)	PUNCT
ma-51	244	1	⊂	⊂	PROPN
ma-51	244	2	f	f	X
ma-51	244	3	(	(	PUNCT
ma-51	244	4	t	t	PROPN
ma-51	244	5	)	)	PUNCT
ma-51	244	6	,	,	PUNCT
ma-51	244	7	where	where	SCONJ
ma-51	244	8	ωω(xn){x	ωω(xn){x	PUNCT
ma-51	244	9	:	:	PUNCT
ma-51	244	10	∃xnk	∃xnk	NOUN
ma-51	245	1	⇀	⇀	X
ma-51	245	2	αx?}is	αx?}is	NUM
ma-51	245	3	the	the	DET
ma-51	245	4	weak	weak	ADJ
ma-51	245	5	limit	limit	NOUN
ma-51	245	6	set	set	VERB
ma-51	245	7	of	of	ADP
ma-51	245	8	{	{	PUNCT
ma-51	245	9	xn	xn	PROPN
ma-51	245	10	}	}	PUNCT
ma-51	245	11	.	.	PUNCT
ma-51	246	1	this	this	PRON
ma-51	246	2	implies	imply	VERB
ma-51	246	3	that	that	SCONJ
ma-51	246	4	the	the	DET
ma-51	246	5	sequence	sequence	NOUN
ma-51	246	6	{	{	PUNCT
ma-51	246	7	xn	xn	NOUN
ma-51	246	8	}	}	PUNCT
ma-51	246	9	converges	converge	VERB
ma-51	246	10	weakly	weakly	ADV
ma-51	246	11	to	to	ADP
ma-51	246	12	a	a	DET
ma-51	246	13	fixed	fixed	ADJ
ma-51	246	14	point	point	NOUN
ma-51	246	15	αx	αx	PROPN
ma-51	246	16	?	?	PUNCT
ma-51	246	17	of	of	ADP
ma-51	246	18	t	t	PROPN
ma-51	246	19	.suppose	.suppose	PUNCT
ma-51	246	20	there	there	PRON
ma-51	246	21	exists	exist	VERB
ma-51	246	22	some	some	DET
ma-51	246	23	subsequences	subsequence	NOUN
ma-51	246	24	{	{	PUNCT
ma-51	246	25	xnk}∞k=0	xnk}∞k=0	PROPN
ma-51	246	26	⊂	⊂	PRON
ma-51	246	27	{	{	PUNCT
ma-51	246	28	xn}∞n=0	xn}∞n=0	VERB
ma-51	246	29	such	such	ADJ
ma-51	246	30	that	that	SCONJ
ma-51	246	31	xnk	xnk	PROPN
ma-51	246	32	⇀	⇀	INTJ
ma-51	246	33	αy	αy	NOUN
ma-51	246	34	?	?	PUNCT
ma-51	246	35	weakly	weakly	ADJ
ma-51	246	36	and	and	CCONJ
ma-51	246	37	αy	αy	NOUN
ma-51	246	38	?	?	PUNCT
ma-51	246	39	6=	6=	NUM
ma-51	246	40	αx	αx	X
ma-51	246	41	?	?	PUNCT
ma-51	246	42	.	.	PUNCT
ma-51	247	1	since	since	SCONJ
ma-51	247	2	limn→∞	limn→∞	PROPN
ma-51	247	3	‖xn	‖xn	PROPN
ma-51	247	4	−	−	PROPN
ma-51	247	5	αv‖	αv‖	PROPN
ma-51	247	6	exists	exist	VERB
ma-51	247	7	for	for	ADP
ma-51	247	8	αv	αv	PROPN
ma-51	247	9	∈	∈	PROPN
ma-51	247	10	f	f	X
ma-51	247	11	(	(	PUNCT
ma-51	247	12	t	t	PROPN
ma-51	247	13	)	)	PUNCT
ma-51	247	14	,	,	PUNCT
ma-51	247	15	by	by	ADP
ma-51	247	16	virtue	virtue	NOUN
ma-51	247	17	of	of	ADP
ma-51	247	18	opial	opial	ADJ
ma-51	247	19	condition	condition	NOUN
ma-51	247	20	on	on	ADP
ma-51	247	21	h	h	NOUN
ma-51	247	22	,	,	PUNCT
ma-51	247	23	wehave	wehave	PROPN
ma-51	247	24	lim	lim	PROPN
ma-51	247	25	n→∞	n→∞	X
ma-51	248	1	‖xn	‖xn	PROPN
ma-51	248	2	−	−	PROPN
ma-51	248	3	αx?‖	αx?‖	PROPN
ma-51	249	1	=	=	SYM
ma-51	249	2	lim	lim	PROPN
ma-51	249	3	n→∞	n→∞	X
ma-51	250	1	‖xnj	‖xnj	INTJ
ma-51	250	2	−	−	NOUN
ma-51	250	3	αx	αx	INTJ
ma-51	250	4	?	?	PUNCT
ma-51	251	1	‖	‖	PROPN
ma-51	251	2	<	<	X
ma-51	251	3	lim	lim	PROPN
ma-51	251	4	n→∞	n→∞	X
ma-51	251	5	‖xnj	‖xnj	INTJ
ma-51	251	6	−	−	NOUN
ma-51	251	7	αy	αy	ADP
ma-51	251	8	?	?	PUNCT
ma-51	251	9	‖	‖	PROPN
ma-51	252	1	=	=	SYM
ma-51	252	2	lim	lim	PROPN
ma-51	252	3	n→∞	n→∞	NUM
ma-51	252	4	‖xnk	‖xnk	PROPN
ma-51	252	5	−	−	PROPN
ma-51	252	6	αy	αy	NOUN
ma-51	252	7	?	?	PUNCT
ma-51	253	1	‖	‖	PROPN
ma-51	253	2	<	<	X
ma-51	253	3	lim	lim	PROPN
ma-51	253	4	n→∞	n→∞	NUM
ma-51	253	5	‖xnk	‖xnk	PROPN
ma-51	253	6	−	−	PROPN
ma-51	253	7	αx	αx	INTJ
ma-51	253	8	?	?	PUNCT
ma-51	253	9	‖	‖	PROPN
ma-51	254	1	=	=	SYM
ma-51	254	2	lim	lim	PROPN
ma-51	254	3	n→∞	n→∞	X
ma-51	255	1	‖xnj	‖xnj	INTJ
ma-51	255	2	−	−	NOUN
ma-51	255	3	αy	αy	X
ma-51	255	4	?	?	PUNCT
ma-51	255	5	‖	‖	PROPN
ma-51	255	6	,	,	PUNCT
ma-51	255	7	which	which	PRON
ma-51	255	8	is	be	AUX
ma-51	255	9	a	a	DET
ma-51	255	10	contradiction	contradiction	NOUN
ma-51	255	11	.	.	PUNCT
ma-51	256	1	consequently	consequently	ADV
ma-51	256	2	,	,	PUNCT
ma-51	256	3	αy	αy	NOUN
ma-51	256	4	?	?	PUNCT
ma-51	256	5	=	=	PUNCT
ma-51	257	1	αx	αx	NOUN
ma-51	257	2	?	?	PUNCT
ma-51	257	3	.	.	PUNCT
ma-51	258	1	this	this	PRON
ma-51	258	2	implies	imply	VERB
ma-51	258	3	that	that	SCONJ
ma-51	258	4	{	{	PUNCT
ma-51	258	5	xnj}∞j=0	xnj}∞j=0	PROPN
ma-51	258	6	converges	converge	VERB
ma-51	258	7	wealy	wealy	NOUN
ma-51	258	8	toa	toa	PROPN
ma-51	258	9	common	common	ADJ
ma-51	258	10	fixed	fix	VERB
ma-51	258	11	point	point	NOUN
ma-51	258	12	of	of	ADP
ma-51	258	13	t.next	t.next	NOUN
ma-51	258	14	,	,	PUNCT
ma-51	258	15	we	we	PRON
ma-51	258	16	prove	prove	VERB
ma-51	258	17	that	that	SCONJ
ma-51	258	18	{	{	PUNCT
ma-51	258	19	xn}∞n=0	xn}∞n=0	X
ma-51	258	20	converges	converge	VERB
ma-51	258	21	strongly	strongly	ADV
ma-51	258	22	to	to	ADP
ma-51	258	23	x?/	x?/	PROPN
ma-51	258	24	let	let	VERB
ma-51	258	25	ξn	ξn	NOUN
ma-51	258	26	=	=	PUNCT
ma-51	258	27	γntyn	γntyn	PROPN
ma-51	259	1	+	+	CCONJ
ma-51	259	2	(	(	PUNCT
ma-51	259	3	1−	1−	NUM
ma-51	259	4	γnxn	γnxn	NOUN
ma-51	259	5	)	)	PUNCT
ma-51	259	6	.	.	PUNCT
ma-51	260	1	then	then	ADV
ma-51	260	2	,	,	PUNCT
ma-51	260	3	from(3.1	from(3.1	ADJ
ma-51	260	4	)	)	PUNCT
ma-51	260	5	,	,	PUNCT
ma-51	260	6	we	we	PRON
ma-51	260	7	obtain	obtain	VERB
ma-51	260	8	xn+1	xn+1	NOUN
ma-51	260	9	=	=	SYM
ma-51	260	10	pk[ξn	pk[ξn	NOUN
ma-51	260	11	−	−	PROPN
ma-51	260	12	δnxn	δnxn	NOUN
ma-51	260	13	]	]	PUNCT
ma-51	260	14	,	,	PUNCT
ma-51	260	15	n	n	X
ma-51	260	16	≥	≥	NOUN
ma-51	260	17	0	0	NUM
ma-51	260	18	.	.	PUNCT
ma-51	261	1	this	this	PRON
ma-51	261	2	implies	imply	VERB
ma-51	261	3	that	that	SCONJ
ma-51	261	4	xn+1	xn+1	ADV
ma-51	261	5	=	=	SYM
ma-51	261	6	pk[ξn	pk[ξn	NOUN
ma-51	261	7	+	+	NUM
ma-51	261	8	δnξn	δnξn	NOUN
ma-51	261	9	+	+	CCONJ
ma-51	261	10	δnξn	δnξn	NOUN
ma-51	261	11	−	−	PROPN
ma-51	261	12	δnxn	δnxn	NOUN
ma-51	261	13	=	=	PUNCT
ma-51	261	14	pk[(1−	pk[(1−	PROPN
ma-51	261	15	δn)ξn	δn)ξn	PUNCT
ma-51	262	1	+	+	NUM
ma-51	262	2	δn(ξn	δn(ξn	PROPN
ma-51	262	3	−	−	PROPN
ma-51	262	4	xn	xn	PROPN
ma-51	262	5	)	)	PUNCT
ma-51	262	6	]	]	PUNCT
ma-51	262	7	.	.	PUNCT
ma-51	263	1	(	(	PUNCT
ma-51	263	2	3.23	3.23	NUM
ma-51	263	3	)	)	PUNCT
ma-51	263	4	observe	observe	VERB
ma-51	263	5	that	that	SCONJ
ma-51	264	1	‖ξn	‖ξn	NUM
ma-51	264	2	−	−	PROPN
ma-51	264	3	αx?‖2	αx?‖2	PROPN
ma-51	264	4	=	=	SYM
ma-51	264	5	‖xn	‖xn	PROPN
ma-51	264	6	−	−	NUM
ma-51	264	7	αx	αx	NOUN
ma-51	264	8	?	?	PUNCT
ma-51	265	1	−	−	PROPN
ma-51	266	1	γn(xn	γn(xn	NOUN
ma-51	266	2	−	−	NOUN
ma-51	266	3	tyn)‖2	tyn)‖2	NOUN
ma-51	266	4	.	.	PUNCT
ma-51	267	1	(	(	PUNCT
ma-51	267	2	3.24)by	3.24)by	NUM
ma-51	267	3	using	use	VERB
ma-51	267	4	the	the	DET
ma-51	267	5	same	same	ADJ
ma-51	267	6	argument	argument	NOUN
ma-51	267	7	as	as	ADP
ma-51	267	8	in	in	ADP
ma-51	267	9	(	(	PUNCT
ma-51	267	10	3.20	3.20	NUM
ma-51	267	11	)	)	PUNCT
ma-51	267	12	,	,	PUNCT
ma-51	267	13	with	with	ADP
ma-51	267	14	αx	αx	X
ma-51	267	15	?	?	PUNCT
ma-51	267	16	=	=	SYM
ma-51	268	1	αq	αq	X
ma-51	268	2	,	,	PUNCT
ma-51	268	3	we	we	PRON
ma-51	268	4	get	get	VERB
ma-51	268	5	,	,	PUNCT
ma-51	268	6	from	from	ADP
ma-51	268	7	(	(	PUNCT
ma-51	268	8	3.24	3.24	NUM
ma-51	268	9	)	)	PUNCT
ma-51	268	10	,	,	PUNCT
ma-51	268	11	that	that	SCONJ
ma-51	268	12	‖ξn	‖ξn	NUM
ma-51	268	13	−	−	PROPN
ma-51	268	14	αx?‖	αx?‖	PROPN
ma-51	268	15	=	=	SYM
ma-51	268	16	‖xn	‖xn	PROPN
ma-51	268	17	−	−	NUM
ma-51	268	18	αx?‖.	αx?‖.	NOUN
ma-51	268	19	(	(	PUNCT
ma-51	268	20	3.25	3.25	NUM
ma-51	268	21	)	)	PUNCT
ma-51	268	22	again	again	ADV
ma-51	268	23	,	,	PUNCT
ma-51	268	24	from	from	ADP
ma-51	268	25	(	(	PUNCT
ma-51	268	26	3.1	3.1	NUM
ma-51	268	27	)	)	PUNCT
ma-51	268	28	,	,	PUNCT
ma-51	268	29	we	we	PRON
ma-51	268	30	obtain	obtain	VERB
ma-51	268	31	‖yn	‖yn	PROPN
ma-51	268	32	−	−	NOUN
ma-51	268	33	xn‖	xn‖	PROPN
ma-51	269	1	=	=	PRON
ma-51	269	2	βn‖xn	βn‖xn	PUNCT
ma-51	269	3	−	−	NUM
ma-51	269	4	txn‖	txn‖	SYM
ma-51	269	5	→	→	SYM
ma-51	269	6	0	0	NUM
ma-51	269	7	as	as	ADP
ma-51	269	8	n	n	PROPN
ma-51	269	9	→∞	→∞	PROPN
ma-51	269	10	,	,	PUNCT
ma-51	269	11	βn	βn	PROPN
ma-51	269	12	∈	∈	PROPN
ma-51	269	13	(	(	PUNCT
ma-51	269	14	0	0	NUM
ma-51	269	15	,	,	PUNCT
ma-51	269	16	1	1	NUM
ma-51	269	17	)	)	PUNCT
ma-51	269	18	.	.	PUNCT
ma-51	270	1	(	(	PUNCT
ma-51	270	2	3.26	3.26	NUM
ma-51	270	3	)	)	PUNCT
ma-51	270	4	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	270	5	eur	eur	PROPN
ma-51	270	6	.	.	PUNCT
ma-51	271	1	j.	j.	PROPN
ma-51	271	2	math	math	PROPN
ma-51	271	3	.	.	PUNCT
ma-51	272	1	anal	anal	PROPN
ma-51	272	2	.	.	PUNCT
ma-51	273	1	10.28924	10.28924	NUM
ma-51	273	2	/	/	SYM
ma-51	273	3	ada	ada	PROPN
ma-51	273	4	/	/	SYM
ma-51	273	5	ma.2.10	ma.2.10	PROPN
ma-51	273	6	10	10	NUM
ma-51	273	7	in	in	ADP
ma-51	273	8	addition	addition	NOUN
ma-51	273	9	,	,	PUNCT
ma-51	273	10	since	since	SCONJ
ma-51	273	11	t	t	PROPN
ma-51	273	12	is	be	AUX
ma-51	273	13	lipschitz	lipschitz	ADJ
ma-51	273	14	,	,	PUNCT
ma-51	273	15	it	it	PRON
ma-51	273	16	follows	follow	VERB
ma-51	273	17	that	that	SCONJ
ma-51	273	18	‖ξn	‖ξn	PROPN
ma-51	273	19	−	−	NOUN
ma-51	273	20	xn‖	xn‖	PROPN
ma-51	274	1	=	=	PUNCT
ma-51	275	1	‖γn[(tyn	‖γn[(tyn	DET
ma-51	275	2	−	−	PROPN
ma-51	275	3	txn)−	txn)−	PROPN
ma-51	275	4	(	(	PUNCT
ma-51	275	5	xn	xn	PROPN
ma-51	275	6	−	−	PROPN
ma-51	275	7	txn)]‖	txn)]‖	PROPN
ma-51	275	8	≤	≤	ADV
ma-51	275	9	γn‖tyn	γn‖tyn	ADV
ma-51	275	10	−	−	NOUN
ma-51	275	11	txn‖	txn‖	PUNCT
ma-51	275	12	−	−	PROPN
ma-51	275	13	γn‖xn	γn‖xn	PUNCT
ma-51	275	14	−	−	PROPN
ma-51	275	15	txn‖	txn‖	SYM
ma-51	275	16	≤	≤	NUM
ma-51	275	17	γnl‖yn	γnl‖yn	ADP
ma-51	275	18	−	−	PROPN
ma-51	275	19	xn‖+	xn‖+	PROPN
ma-51	275	20	γn‖xn	γn‖xn	X
ma-51	276	1	−	−	SCONJ
ma-51	276	2	txn‖	txn‖	SYM
ma-51	276	3	→	→	SYM
ma-51	276	4	0	0	NUM
ma-51	276	5	as	as	ADP
ma-51	276	6	n	n	X
ma-51	276	7	→∞.	→∞.	PROPN
ma-51	276	8	(	(	PUNCT
ma-51	276	9	3.27	3.27	NUM
ma-51	276	10	)	)	PUNCT
ma-51	276	11	now	now	ADV
ma-51	276	12	,	,	PUNCT
ma-51	276	13	using	use	VERB
ma-51	276	14	(	(	PUNCT
ma-51	276	15	3.23	3.23	NUM
ma-51	276	16	)	)	PUNCT
ma-51	276	17	,	,	PUNCT
ma-51	276	18	we	we	PRON
ma-51	276	19	get	get	VERB
ma-51	276	20	‖xn+1	‖xn+1	PUNCT
ma-51	276	21	−	−	PROPN
ma-51	276	22	αx?‖2	αx?‖2	PROPN
ma-51	276	23	≤	≤	NOUN
ma-51	276	24	‖(1−	‖(1−	PROPN
ma-51	276	25	δn)ξn	δn)ξn	PUNCT
ma-51	276	26	+	+	NUM
ma-51	276	27	δn(ξn	δn(ξn	PROPN
ma-51	276	28	−	−	PROPN
ma-51	276	29	xn)−	xn)−	X
ma-51	277	1	αx?‖2	αx?‖2	X
ma-51	277	2	=	=	SYM
ma-51	277	3	‖(1−	‖(1−	PROPN
ma-51	277	4	δn)(ξn	δn)(ξn	NUM
ma-51	277	5	−	−	PROPN
ma-51	277	6	αx	αx	NOUN
ma-51	277	7	?	?	PUNCT
ma-51	277	8	)	)	PUNCT
ma-51	278	1	+	+	CCONJ
ma-51	278	2	δn(ξn	δn(ξn	PROPN
ma-51	278	3	−	−	PROPN
ma-51	278	4	xn)−	xn)−	PUNCT
ma-51	278	5	δnαx?‖2	δnαx?‖2	PROPN
ma-51	278	6	,	,	PUNCT
ma-51	278	7	which	which	PRON
ma-51	278	8	by	by	ADP
ma-51	278	9	lemma	lemma	PROPN
ma-51	278	10	2.3	2.3	NUM
ma-51	278	11	yields	yield	NOUN
ma-51	278	12	‖xn+1	‖xn+1	PUNCT
ma-51	278	13	−	−	PROPN
ma-51	278	14	αx?‖2	αx?‖2	PROPN
ma-51	278	15	≤	≤	PROPN
ma-51	278	16	‖(1−	‖(1−	PROPN
ma-51	278	17	δn)(ξn	δn)(ξn	NUM
ma-51	278	18	−	−	PROPN
ma-51	278	19	αx	αx	NOUN
ma-51	278	20	?	?	PUNCT
ma-51	278	21	)	)	PUNCT
ma-51	279	1	+	+	CCONJ
ma-51	280	1	δn(ξn	δn(ξn	PROPN
ma-51	280	2	−	−	PROPN
ma-51	280	3	xn)‖2	xn)‖2	PROPN
ma-51	281	1	−	−	PROPN
ma-51	281	2	2δn〈αx	2δn〈αx	NOUN
ma-51	281	3	?	?	PUNCT
ma-51	281	4	,	,	PUNCT
ma-51	281	5	xn+1	xn+1	NUM
ma-51	281	6	−	−	NOUN
ma-51	281	7	αx	αx	INTJ
ma-51	281	8	?	?	PUNCT
ma-51	281	9	〉	〉	NOUN
ma-51	281	10	=	=	SYM
ma-51	281	11	(	(	PUNCT
ma-51	281	12	1−	1−	NUM
ma-51	281	13	δn)‖ξn	δn)‖ξn	NOUN
ma-51	281	14	−	−	PROPN
ma-51	281	15	αx?‖2	αx?‖2	PROPN
ma-51	281	16	+	+	CCONJ
ma-51	281	17	δn‖ξn	δn‖ξn	ADJ
ma-51	281	18	−	−	PROPN
ma-51	281	19	xn‖2	xn‖2	PROPN
ma-51	281	20	−	−	PROPN
ma-51	281	21	δn(1−	δn(1−	PROPN
ma-51	281	22	δn)‖xn	δn)‖xn	PROPN
ma-51	281	23	−	−	PROPN
ma-51	281	24	αx?‖2	αx?‖2	PROPN
ma-51	281	25	−2δn〈αx	−2δn〈αx	PROPN
ma-51	281	26	?	?	PUNCT
ma-51	281	27	,	,	PUNCT
ma-51	281	28	xn+1	xn+1	NUM
ma-51	281	29	−	−	NOUN
ma-51	282	1	αx	αx	INTJ
ma-51	282	2	?	?	SYM
ma-51	282	3	〉	〉	NOUN
ma-51	282	4	≤	≤	NOUN
ma-51	282	5	(	(	PUNCT
ma-51	282	6	1−	1−	NUM
ma-51	282	7	δn)‖ξn	δn)‖ξn	NOUN
ma-51	282	8	−	−	PROPN
ma-51	282	9	αx?‖2	αx?‖2	PROPN
ma-51	282	10	+	+	PROPN
ma-51	282	11	‖ξn	‖ξn	PROPN
ma-51	282	12	−	−	PROPN
ma-51	282	13	xn‖2	xn‖2	PROPN
ma-51	282	14	−	−	PROPN
ma-51	282	15	2δn〈αx	2δn〈αx	NOUN
ma-51	282	16	?	?	PUNCT
ma-51	282	17	,	,	PUNCT
ma-51	282	18	xn+1	xn+1	NUM
ma-51	282	19	−	−	NOUN
ma-51	282	20	αx	αx	INTJ
ma-51	282	21	?	?	PUNCT
ma-51	282	22	〉	〉	NOUN
ma-51	282	23	=	=	SYM
ma-51	282	24	(	(	PUNCT
ma-51	282	25	1−	1−	NUM
ma-51	282	26	δn)‖ξn	δn)‖ξn	NOUN
ma-51	282	27	−	−	PROPN
ma-51	282	28	αx?‖2	αx?‖2	PROPN
ma-51	282	29	−	−	PROPN
ma-51	282	30	2δn〈αx	2δn〈αx	NUM
ma-51	282	31	?	?	PUNCT
ma-51	282	32	,	,	PUNCT
ma-51	282	33	xn+1	xn+1	NUM
ma-51	282	34	−	−	NOUN
ma-51	283	1	αx	αx	INTJ
ma-51	283	2	?	?	X
ma-51	283	3	〉	〉	NOUN
ma-51	283	4	(	(	PUNCT
ma-51	283	5	by	by	ADP
ma-51	283	6	(	(	PUNCT
ma-51	283	7	3.27	3.27	NUM
ma-51	283	8	)	)	PUNCT
ma-51	283	9	)	)	PUNCT
ma-51	283	10	(	(	PUNCT
ma-51	283	11	3.28	3.28	NUM
ma-51	283	12	)	)	PUNCT
ma-51	283	13	≤	≤	NOUN
ma-51	283	14	(	(	PUNCT
ma-51	283	15	1−	1−	NUM
ma-51	283	16	δn)‖ξn	δn)‖ξn	NOUN
ma-51	283	17	−	−	PROPN
ma-51	283	18	αx?‖2	αx?‖2	NUM
ma-51	283	19	(	(	PUNCT
ma-51	283	20	3.29	3.29	NUM
ma-51	283	21	)	)	PUNCT
ma-51	283	22	(	(	PUNCT
ma-51	283	23	3.29	3.29	NUM
ma-51	283	24	)	)	PUNCT
ma-51	284	1	and	and	CCONJ
ma-51	284	2	lemma	lemma	PROPN
ma-51	284	3	2.2	2.2	NUM
ma-51	284	4	imply	imply	NOUN
ma-51	284	5	that	that	SCONJ
ma-51	284	6	xn	xn	PROPN
ma-51	285	1	→	→	SYM
ma-51	285	2	αx	αx	NOUN
ma-51	285	3	?	?	PUNCT
ma-51	286	1	as	as	ADP
ma-51	286	2	n	n	X
ma-51	286	3	→∞.case	→∞.case	NOUN
ma-51	286	4	b	b	X
ma-51	286	5	:	:	PUNCT
ma-51	286	6	assume	assume	VERB
ma-51	286	7	that	that	SCONJ
ma-51	286	8	{	{	PUNCT
ma-51	286	9	‖xn	‖xn	PROPN
ma-51	286	10	−	−	PROPN
ma-51	286	11	αq‖}∞n=0	αq‖}∞n=0	PROPN
ma-51	286	12	is	be	AUX
ma-51	286	13	not	not	PART
ma-51	286	14	a	a	DET
ma-51	286	15	monotonically	monotonically	ADV
ma-51	286	16	increasing	increase	VERB
ma-51	286	17	sequence	sequence	NOUN
ma-51	286	18	.	.	PUNCT
ma-51	287	1	set	set	VERB
ma-51	287	2	vn	vn	PROPN
ma-51	287	3	=	=	SYM
ma-51	288	1	‖xn	‖xn	PROPN
ma-51	288	2	−	−	NOUN
ma-51	288	3	αq‖2	αq‖2	NOUN
ma-51	289	1	and	and	CCONJ
ma-51	289	2	let	let	VERB
ma-51	289	3	τ	τ	PROPN
ma-51	289	4	:	:	PUNCT
ma-51	289	5	n	n	CCONJ
ma-51	289	6	−→	−→	NOUN
ma-51	289	7	n	n	AUX
ma-51	289	8	be	be	AUX
ma-51	289	9	a	a	DET
ma-51	289	10	mapping	mapping	NOUN
ma-51	289	11	defined	define	VERB
ma-51	289	12	by	by	ADP
ma-51	289	13	τn	τn	ADP
ma-51	289	14	=	=	PUNCT
ma-51	289	15	max{k	max{k	PROPN
ma-51	289	16	∈	∈	PROPN
ma-51	289	17	n	n	NOUN
ma-51	290	1	:	:	PUNCT
ma-51	290	2	k	k	PROPN
ma-51	290	3	≤	≤	PROPN
ma-51	290	4	n	n	CCONJ
ma-51	290	5	,	,	PUNCT
ma-51	290	6	vn	vn	VERB
ma-51	290	7	≤	≤	ADJ
ma-51	290	8	vn+1},∀n	vn+1},∀n	PROPN
ma-51	290	9	≥	≥	X
ma-51	290	10	n0	n0	NUM
ma-51	290	11	,	,	PUNCT
ma-51	290	12	for	for	ADP
ma-51	290	13	some	some	DET
ma-51	290	14	n0	n0	ADJ
ma-51	290	15	large	large	ADJ
ma-51	290	16	enough	enough	ADV
ma-51	290	17	.	.	PUNCT
ma-51	291	1	obviously	obviously	ADV
ma-51	291	2	,	,	PUNCT
ma-51	291	3	{	{	PUNCT
ma-51	291	4	τn}∞n=0	τn}∞n=0	X
ma-51	291	5	is	be	AUX
ma-51	291	6	a	a	DET
ma-51	291	7	nondecreasing	nondecrease	VERB
ma-51	291	8	sequence	sequence	NOUN
ma-51	291	9	given	give	VERB
ma-51	291	10	that	that	PRON
ma-51	291	11	τn	τn	NOUN
ma-51	291	12	→	→	SYM
ma-51	291	13	∞	∞	PROPN
ma-51	291	14	as	as	ADP
ma-51	291	15	n	n	PROPN
ma-51	291	16	→∞	→∞	PROPN
ma-51	291	17	and	and	CCONJ
ma-51	291	18	vτn	vτn	ADP
ma-51	291	19	≤	≤	NUM
ma-51	291	20	vτn+1	vτn+1	PROPN
ma-51	291	21	for	for	ADP
ma-51	291	22	all	all	DET
ma-51	291	23	n	n	PRON
ma-51	291	24	≥	≥	NOUN
ma-51	291	25	n0	n0	NUM
ma-51	291	26	.	.	PUNCT
ma-51	292	1	from	from	ADP
ma-51	292	2	(	(	PUNCT
ma-51	292	3	3.22	3.22	NUM
ma-51	292	4	)	)	PUNCT
ma-51	292	5	,	,	PUNCT
ma-51	292	6	‖xτ(n	‖xτ(n	X
ma-51	292	7	)	)	PUNCT
ma-51	292	8	−	−	NOUN
ma-51	292	9	txτ(n)‖2	txτ(n)‖2	NOUN
ma-51	292	10	≤	≤	PROPN
ma-51	292	11	δτ(n)b	δτ(n)b	NUM
ma-51	292	12	(	(	PUNCT
ma-51	292	13	1−	1−	NUM
ma-51	292	14	γτ(n	γτ(n	NOUN
ma-51	292	15	)	)	PUNCT
ma-51	292	16	−	−	NOUN
ma-51	292	17	γτ(n)l)β2	γτ(n)l)β2	X
ma-51	292	18	τ(n	τ(n	NOUN
ma-51	292	19	)	)	PUNCT
ma-51	292	20	γτ(n)l	γτ(n)l	PROPN
ma-51	292	21	→	→	SYM
ma-51	292	22	0	0	NUM
ma-51	292	23	as	as	ADP
ma-51	292	24	n	n	X
ma-51	292	25	→∞.	→∞.	X
ma-51	292	26	(	(	PUNCT
ma-51	292	27	3.30	3.30	NUM
ma-51	292	28	)	)	PUNCT
ma-51	292	29	therefore	therefore	ADV
ma-51	292	30	,	,	PUNCT
ma-51	292	31	limn→∞	limn→∞	PROPN
ma-51	292	32	‖xτ(n	‖xτ(n	X
ma-51	292	33	)	)	PUNCT
ma-51	292	34	−	−	NOUN
ma-51	292	35	txτ(n)‖	txτ(n)‖	NOUN
ma-51	292	36	=	=	SYM
ma-51	292	37	0	0	X
ma-51	292	38	.	.	X
ma-51	292	39	using	use	VERB
ma-51	292	40	similar	similar	ADJ
ma-51	292	41	argument	argument	NOUN
ma-51	292	42	as	as	SCONJ
ma-51	292	43	case	case	NOUN
ma-51	292	44	a	a	DET
ma-51	292	45	above	above	ADJ
ma-51	292	46	,	,	PUNCT
ma-51	292	47	we	we	PRON
ma-51	292	48	concludethat	concludethat	X
ma-51	292	49	{	{	PUNCT
ma-51	292	50	xτ(n	xτ(n	NUM
ma-51	292	51	)	)	PUNCT
ma-51	292	52	}	}	PUNCT
ma-51	292	53	→	→	SYM
ma-51	292	54	αx	αx	X
ma-51	292	55	?	?	PUNCT
ma-51	293	1	→∞.from	→∞.from	ADP
ma-51	293	2	(	(	PUNCT
ma-51	293	3	3.28	3.28	NUM
ma-51	293	4	)	)	PUNCT
ma-51	293	5	,	,	PUNCT
ma-51	293	6	we	we	PRON
ma-51	293	7	have	have	VERB
ma-51	293	8	0	0	NUM
ma-51	293	9	≤	≤	PROPN
ma-51	293	10	‖xτ(n)+1	‖xτ(n)+1	PROPN
ma-51	293	11	−	−	PROPN
ma-51	293	12	αx?‖2	αx?‖2	PROPN
ma-51	293	13	−	−	PROPN
ma-51	293	14	‖xτ(n	‖xτ(n	NOUN
ma-51	293	15	)	)	PUNCT
ma-51	293	16	−	−	PROPN
ma-51	293	17	αx?‖2	αx?‖2	PROPN
ma-51	293	18	≤	≤	PROPN
ma-51	293	19	δτ(n)[2〈αx	δτ(n)[2〈αx	NOUN
ma-51	293	20	?	?	PUNCT
ma-51	294	1	−	−	PUNCT
ma-51	295	1	xτ(n)+1	xτ(n)+1	PROPN
ma-51	295	2	−	−	PROPN
ma-51	295	3	‖xτ(n	‖xτ(n	PROPN
ma-51	295	4	)	)	PUNCT
ma-51	295	5	−	−	NOUN
ma-51	296	1	αx?‖2	αx?‖2	PROPN
ma-51	296	2	]	]	PUNCT
ma-51	296	3	,	,	PUNCT
ma-51	296	4	(	(	PUNCT
ma-51	296	5	3.31	3.31	NUM
ma-51	296	6	)	)	PUNCT
ma-51	296	7	for	for	ADP
ma-51	296	8	δτ(n	δτ(n	NOUN
ma-51	296	9	)	)	PUNCT
ma-51	296	10	∈	∈	PROPN
ma-51	296	11	(	(	PUNCT
ma-51	296	12	0	0	NUM
ma-51	296	13	,	,	PUNCT
ma-51	296	14	1	1	NUM
ma-51	296	15	)	)	PUNCT
ma-51	296	16	.	.	PUNCT
ma-51	297	1	hence	hence	ADV
ma-51	297	2	,	,	PUNCT
ma-51	297	3	limn→∞	limn→∞	PROPN
ma-51	297	4	‖xτ(n	‖xτ(n	X
ma-51	297	5	)	)	PUNCT
ma-51	297	6	−	−	PROPN
ma-51	297	7	αx?‖2	αx?‖2	PROPN
ma-51	297	8	=	=	SYM
ma-51	297	9	0	0	X
ma-51	297	10	.	.	PUNCT
ma-51	298	1	this	this	PRON
ma-51	298	2	implies	imply	VERB
ma-51	298	3	that	that	SCONJ
ma-51	298	4	limn→∞	limn→∞	PROPN
ma-51	298	5	vτ(n	vτ(n	PUNCT
ma-51	298	6	)	)	PUNCT
ma-51	298	7	=	=	SYM
ma-51	298	8	limn→∞	limn→∞	PROPN
ma-51	298	9	vτ(n)+1	vτ(n)+1	NOUN
ma-51	298	10	=	=	SYM
ma-51	298	11	0	0	X
ma-51	298	12	.	.	PUNCT
ma-51	299	1	in	in	ADP
ma-51	299	2	addition	addition	NOUN
ma-51	299	3	,	,	PUNCT
ma-51	299	4	for	for	ADP
ma-51	299	5	n	n	PRON
ma-51	299	6	≥	≥	NOUN
ma-51	299	7	n0	n0	NUM
ma-51	299	8	,	,	PUNCT
ma-51	299	9	it	it	PRON
ma-51	299	10	is	be	AUX
ma-51	299	11	easy	easy	ADJ
ma-51	299	12	to	to	PART
ma-51	299	13	see	see	VERB
ma-51	299	14	that	that	PRON
ma-51	299	15	vτ(n	vτ(n	PUNCT
ma-51	299	16	)	)	PUNCT
ma-51	300	1	=	=	PUNCT
ma-51	300	2	vτ(n)+1	vτ(n)+1	NOUN
ma-51	300	3	if	if	SCONJ
ma-51	300	4	n	n	PROPN
ma-51	300	5	6=	6=	ADP
ma-51	300	6	τ(n)(i.e	τ(n)(i.e	NOUN
ma-51	300	7	.	.	NOUN
ma-51	300	8	,	,	PUNCT
ma-51	300	9	τ(n	τ(n	PROPN
ma-51	300	10	)	)	PUNCT
ma-51	300	11	<	<	X
ma-51	300	12	n	n	CCONJ
ma-51	300	13	)	)	PUNCT
ma-51	300	14	because	because	SCONJ
ma-51	300	15	vj	vj	INTJ
ma-51	300	16	>	>	X
ma-51	300	17	vj+1	vj+1	PROPN
ma-51	300	18	,	,	PUNCT
ma-51	300	19	f	f	NOUN
ma-51	300	20	or	or	CCONJ
ma-51	300	21	τ(n	τ(n	PROPN
ma-51	300	22	)	)	PUNCT
ma-51	300	23	+	+	CCONJ
ma-51	300	24	1	1	NUM
ma-51	300	25	≤	≤	NOUN
ma-51	300	26	n.	n.	NOUN
ma-51	300	27	consequently	consequently	ADV
ma-51	300	28	.	.	PUNCT
ma-51	301	1	we	we	PRON
ma-51	301	2	obtain	obtain	VERB
ma-51	301	3	,	,	PUNCT
ma-51	301	4	for	for	ADP
ma-51	301	5	all	all	DET
ma-51	301	6	n	n	PRON
ma-51	301	7	≥	≥	NOUN
ma-51	301	8	n0	n0	NUM
ma-51	301	9	,	,	PUNCT
ma-51	301	10	0	0	NUM
ma-51	301	11	≤	≤	NUM
ma-51	301	12	vτ(n)max{vτ(n	vτ(n)max{vτ(n	NOUN
ma-51	301	13	)	)	PUNCT
ma-51	301	14	,	,	PUNCT
ma-51	301	15	vτ(n)+1	vτ(n)+1	ADV
ma-51	301	16	}	}	PUNCT
ma-51	301	17	=	=	PUNCT
ma-51	301	18	vτ(n)+1	vτ(n)+1	NOUN
ma-51	301	19	.	.	PUNCT
ma-51	302	1	hence	hence	ADV
ma-51	302	2	,	,	PUNCT
ma-51	302	3	limn→∞	limn→∞	PROPN
ma-51	302	4	vn	vn	PROPN
ma-51	302	5	=	=	SYM
ma-51	302	6	0	0	PROPN
ma-51	302	7	.	.	PUNCT
ma-51	303	1	that	that	PRON
ma-51	303	2	is	is	ADV
ma-51	303	3	,	,	PUNCT
ma-51	303	4	{	{	PUNCT
ma-51	303	5	xn}∞n=0	xn}∞n=0	X
ma-51	303	6	converges	converge	VERB
ma-51	303	7	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	303	8	eur	eur	PROPN
ma-51	303	9	.	.	PUNCT
ma-51	304	1	j.	j.	PROPN
ma-51	304	2	math	math	PROPN
ma-51	304	3	.	.	PUNCT
ma-51	305	1	anal	anal	PROPN
ma-51	305	2	.	.	PUNCT
ma-51	306	1	10.28924	10.28924	NUM
ma-51	306	2	/	/	SYM
ma-51	306	3	ada	ada	PROPN
ma-51	306	4	/	/	SYM
ma-51	306	5	ma.2.10	ma.2.10	PROPN
ma-51	306	6	11strongly	11strongly	ADV
ma-51	306	7	to	to	ADP
ma-51	306	8	αx	αx	PRON
ma-51	306	9	?	?	PUNCT
ma-51	306	10	,	,	PUNCT
ma-51	306	11	and	and	CCONJ
ma-51	306	12	this	this	PRON
ma-51	306	13	completes	complete	VERB
ma-51	306	14	the	the	DET
ma-51	306	15	proof	proof	NOUN
ma-51	306	16	.	.	PUNCT
ma-51	307	1	�	�	PROPN
ma-51	307	2	the	the	DET
ma-51	307	3	following	follow	VERB
ma-51	307	4	corollaries	corollary	NOUN
ma-51	307	5	are	be	AUX
ma-51	307	6	immediate	immediate	ADJ
ma-51	307	7	consequence	consequence	NOUN
ma-51	307	8	of	of	ADP
ma-51	307	9	theorem	theorem	ADJ
ma-51	307	10	3.1	3.1	NUM
ma-51	307	11	.	.	PUNCT
ma-51	307	12	corollary	corollary	ADJ
ma-51	307	13	3.2	3.2	NUM
ma-51	307	14	.	.	PUNCT
ma-51	308	1	let	let	VERB
ma-51	308	2	h	h	PRON
ma-51	308	3	be	be	AUX
ma-51	308	4	a	a	DET
ma-51	308	5	real	real	ADJ
ma-51	308	6	hilbert	hilbert	NOUN
ma-51	308	7	space	space	NOUN
ma-51	308	8	,	,	PUNCT
ma-51	308	9	k	k	PROPN
ma-51	308	10	a	a	DET
ma-51	308	11	nonempty	nonempty	ADV
ma-51	308	12	closed	close	VERB
ma-51	308	13	convex	convex	NOUN
ma-51	308	14	subset	subset	NOUN
ma-51	308	15	of	of	ADP
ma-51	308	16	h	h	PROPN
ma-51	308	17	and	and	CCONJ
ma-51	308	18	t	t	PROPN
ma-51	308	19	:	:	PUNCT
ma-51	309	1	k	k	X
ma-51	309	2	−→	−→	NOUN
ma-51	309	3	k	k	PROPN
ma-51	309	4	an	an	DET
ma-51	309	5	l	l	ADJ
ma-51	309	6	-	-	ADJ
ma-51	309	7	lipschitz	lipschitz	ADJ
ma-51	309	8	hemicontractive	hemicontractive	ADJ
ma-51	309	9	mapping	mapping	NOUN
ma-51	309	10	.	.	PUNCT
ma-51	310	1	for	for	ADP
ma-51	310	2	any	any	DET
ma-51	310	3	arbitrary	arbitrary	ADJ
ma-51	310	4	x0	x0	PROPN
ma-51	310	5	∈	∈	PROPN
ma-51	310	6	h	h	NOUN
ma-51	310	7	,	,	PUNCT
ma-51	310	8	define	define	VERB
ma-51	310	9	the	the	DET
ma-51	310	10	sequence	sequence	NOUN
ma-51	310	11	{	{	PUNCT
ma-51	310	12	xn}∞n=0	xn}∞n=0	X
ma-51	310	13	iteratively	iteratively	ADV
ma-51	310	14	as	as	ADP
ma-51	310	15	follows:	follows:	NOUN
ma-51	310	16	xn+1	xn+1	PROPN
ma-51	311	1	=	=	PUNCT
ma-51	312	1	pk[(1−	pk[(1−	PROPN
ma-51	312	2	αn	αn	ADP
ma-51	313	1	−	−	PROPN
ma-51	313	2	γn)xn	γn)xn	PROPN
ma-51	313	3	+	+	CCONJ
ma-51	313	4	γntyn	γntyn	PROPN
ma-51	313	5	]	]	X
ma-51	313	6	yn	yn	PROPN
ma-51	313	7	=	=	SYM
ma-51	313	8	(	(	PUNCT
ma-51	313	9	1−	1−	NUM
ma-51	313	10	βn)xn	βn)xn	PROPN
ma-51	313	11	+	+	CCONJ
ma-51	313	12	βntxn	βntxn	ADJ
ma-51	313	13	,	,	PUNCT
ma-51	313	14	n	n	PRON
ma-51	313	15	≥	≥	NOUN
ma-51	313	16	1	1	NUM
ma-51	313	17	,	,	PUNCT
ma-51	313	18	(	(	PUNCT
ma-51	313	19	3.32	3.32	NUM
ma-51	313	20	)	)	PUNCT
ma-51	313	21	where	where	SCONJ
ma-51	313	22	the	the	DET
ma-51	313	23	sequences	sequence	NOUN
ma-51	313	24	{	{	PUNCT
ma-51	313	25	δn}∞n=0	δn}∞n=0	X
ma-51	313	26	,	,	PUNCT
ma-51	313	27	{	{	PUNCT
ma-51	313	28	γn}∞n=0	γn}∞n=0	VERB
ma-51	313	29	,	,	PUNCT
ma-51	313	30	{	{	PUNCT
ma-51	313	31	βn}∞n=0	βn}∞n=0	X
ma-51	313	32	∈	∈	PROPN
ma-51	313	33	(	(	PUNCT
ma-51	313	34	0	0	NUM
ma-51	313	35	,	,	PUNCT
ma-51	313	36	1	1	X
ma-51	313	37	)	)	PUNCT
ma-51	313	38	satisfy	satisfy	VERB
ma-51	313	39	the	the	DET
ma-51	313	40	following	follow	VERB
ma-51	313	41	conditions	condition	NOUN
ma-51	313	42	:	:	PUNCT
ma-51	313	43	(	(	PUNCT
ma-51	313	44	i	i	NOUN
ma-51	313	45	)	)	PUNCT
ma-51	313	46	0	0	PUNCT
ma-51	313	47	<	<	X
ma-51	313	48	δ	δ	PROPN
ma-51	313	49	≤	≤	NUM
ma-51	313	50	δn	δn	ADJ
ma-51	313	51	≤	≤	NUM
ma-51	313	52	βn	βn	NOUN
ma-51	313	53	≤	≤	NUM
ma-51	313	54	γn	γn	ADP
ma-51	313	55	≤	≤	NUM
ma-51	313	56	γ	γ	X
ma-51	313	57	≤	≤	NOUN
ma-51	313	58	1−	1−	NUM
ma-51	313	59	δ	δ	NOUN
ma-51	313	60	1	1	NUM
ma-51	313	61	+	+	CCONJ
ma-51	313	62	l2	l2	NOUN
ma-51	313	63	;	;	PUNCT
ma-51	313	64	(	(	PUNCT
ma-51	314	1	i	i	PRON
ma-51	314	2	i	i	PROPN
ma-51	314	3	)	)	PUNCT
ma-51	314	4	limn→∞	limn→∞	VERB
ma-51	314	5	δn	δn	NOUN
ma-51	314	6	=	=	SYM
ma-51	314	7	0	0	NUM
ma-51	314	8	and	and	CCONJ
ma-51	314	9	∑∞	∑∞	NOUN
ma-51	314	10	n=0	n=0	X
ma-51	314	11	δn	δn	NOUN
ma-51	314	12	=	=	SYM
ma-51	314	13	∞.	∞.	PROPN
ma-51	314	14	then	then	ADV
ma-51	314	15	,	,	PUNCT
ma-51	314	16	the	the	DET
ma-51	314	17	sequence	sequence	NOUN
ma-51	314	18	{	{	PUNCT
ma-51	314	19	xn}∞n=0	xn}∞n=0	VERB
ma-51	314	20	generated	generate	VERB
ma-51	314	21	by	by	ADP
ma-51	314	22	(	(	PUNCT
ma-51	314	23	3.32	3.32	NUM
ma-51	314	24	)	)	PUNCT
ma-51	314	25	weakly	weakly	ADJ
ma-51	314	26	and	and	CCONJ
ma-51	314	27	strongly	strongly	ADV
ma-51	314	28	converges	converge	VERB
ma-51	314	29	to	to	ADP
ma-51	314	30	the	the	DET
ma-51	314	31	fixed	fix	VERB
ma-51	314	32	point	point	NOUN
ma-51	314	33	of	of	ADP
ma-51	314	34	t	t	PROPN
ma-51	314	35	.	.	PUNCT
ma-51	315	1	corollary	corollary	ADJ
ma-51	315	2	3.3	3.3	NUM
ma-51	315	3	.	.	PUNCT
ma-51	316	1	let	let	VERB
ma-51	316	2	h	h	PRON
ma-51	316	3	be	be	AUX
ma-51	316	4	a	a	DET
ma-51	316	5	real	real	ADJ
ma-51	316	6	hilbert	hilbert	NOUN
ma-51	316	7	space	space	NOUN
ma-51	316	8	,	,	PUNCT
ma-51	316	9	k	k	PROPN
ma-51	316	10	a	a	DET
ma-51	316	11	nonempty	nonempty	ADV
ma-51	316	12	closed	close	VERB
ma-51	316	13	convex	convex	NOUN
ma-51	316	14	subset	subset	NOUN
ma-51	316	15	of	of	ADP
ma-51	316	16	h	h	PROPN
ma-51	316	17	and	and	CCONJ
ma-51	316	18	t	t	PROPN
ma-51	316	19	:	:	PUNCT
ma-51	317	1	k	k	X
ma-51	317	2	−→	−→	PROPN
ma-51	317	3	k	k	PROPN
ma-51	317	4	is	be	AUX
ma-51	317	5	α	α	PRON
ma-51	317	6	-	-	ADJ
ma-51	317	7	demicontractive	demicontractive	ADJ
ma-51	317	8	mapping	mapping	NOUN
ma-51	317	9	.	.	PUNCT
ma-51	318	1	for	for	ADP
ma-51	318	2	any	any	DET
ma-51	318	3	arbitrary	arbitrary	ADJ
ma-51	318	4	x0	x0	PROPN
ma-51	318	5	∈	∈	PROPN
ma-51	318	6	h	h	NOUN
ma-51	318	7	,	,	PUNCT
ma-51	318	8	define	define	VERB
ma-51	318	9	the	the	DET
ma-51	318	10	sequence	sequence	NOUN
ma-51	318	11	{	{	PUNCT
ma-51	318	12	xn}∞n=0	xn}∞n=0	X
ma-51	318	13	iteratively	iteratively	ADV
ma-51	318	14	as	as	ADP
ma-51	318	15	follows:	follows:	NOUN
ma-51	318	16	xn+1	xn+1	PROPN
ma-51	319	1	=	=	PUNCT
ma-51	320	1	pk[(1−	pk[(1−	PROPN
ma-51	320	2	αn	αn	ADP
ma-51	321	1	−	−	PROPN
ma-51	321	2	γn)xn	γn)xn	PROPN
ma-51	321	3	+	+	CCONJ
ma-51	321	4	γntyn	γntyn	PROPN
ma-51	321	5	]	]	X
ma-51	321	6	yn	yn	PROPN
ma-51	321	7	=	=	SYM
ma-51	321	8	(	(	PUNCT
ma-51	321	9	1−	1−	NUM
ma-51	321	10	βn)xn	βn)xn	PROPN
ma-51	321	11	+	+	CCONJ
ma-51	321	12	βntxn	βntxn	ADJ
ma-51	321	13	,	,	PUNCT
ma-51	321	14	n	n	PRON
ma-51	321	15	≥	≥	NOUN
ma-51	321	16	1	1	NUM
ma-51	321	17	,	,	PUNCT
ma-51	321	18	(	(	PUNCT
ma-51	321	19	3.33	3.33	NUM
ma-51	321	20	)	)	PUNCT
ma-51	321	21	where	where	SCONJ
ma-51	321	22	the	the	DET
ma-51	321	23	sequences	sequence	NOUN
ma-51	321	24	{	{	PUNCT
ma-51	321	25	δn}∞n=0	δn}∞n=0	X
ma-51	321	26	,	,	PUNCT
ma-51	321	27	{	{	PUNCT
ma-51	321	28	γn}∞n=0	γn}∞n=0	VERB
ma-51	321	29	,	,	PUNCT
ma-51	321	30	{	{	PUNCT
ma-51	321	31	βn}∞n=0	βn}∞n=0	X
ma-51	321	32	∈	∈	PROPN
ma-51	321	33	(	(	PUNCT
ma-51	321	34	0	0	NUM
ma-51	321	35	,	,	PUNCT
ma-51	321	36	1	1	X
ma-51	321	37	)	)	PUNCT
ma-51	321	38	satisfy	satisfy	VERB
ma-51	321	39	the	the	DET
ma-51	321	40	following	follow	VERB
ma-51	321	41	conditions	condition	NOUN
ma-51	321	42	:	:	PUNCT
ma-51	321	43	(	(	PUNCT
ma-51	321	44	i	i	NOUN
ma-51	321	45	)	)	PUNCT
ma-51	321	46	0	0	PUNCT
ma-51	321	47	<	<	X
ma-51	321	48	δ	δ	PROPN
ma-51	321	49	≤	≤	NUM
ma-51	321	50	δn	δn	ADJ
ma-51	321	51	≤	≤	NUM
ma-51	321	52	βn	βn	NOUN
ma-51	321	53	≤	≤	NUM
ma-51	321	54	γn	γn	ADP
ma-51	321	55	≤	≤	NUM
ma-51	321	56	γ	γ	X
ma-51	321	57	≤	≤	NOUN
ma-51	321	58	1−	1−	NUM
ma-51	321	59	δ	δ	NOUN
ma-51	321	60	1	1	NUM
ma-51	321	61	+	+	CCONJ
ma-51	321	62	l2	l2	NOUN
ma-51	321	63	;	;	PUNCT
ma-51	321	64	(	(	PUNCT
ma-51	322	1	i	i	PRON
ma-51	322	2	i	i	PROPN
ma-51	322	3	)	)	PUNCT
ma-51	322	4	limn→∞	limn→∞	VERB
ma-51	322	5	δn	δn	NOUN
ma-51	322	6	=	=	SYM
ma-51	322	7	0	0	NUM
ma-51	322	8	and	and	CCONJ
ma-51	322	9	∑∞	∑∞	NOUN
ma-51	322	10	n=0	n=0	X
ma-51	322	11	δn	δn	NOUN
ma-51	322	12	=	=	SYM
ma-51	322	13	∞.	∞.	PROPN
ma-51	322	14	then	then	ADV
ma-51	322	15	,	,	PUNCT
ma-51	322	16	the	the	DET
ma-51	322	17	sequence	sequence	NOUN
ma-51	322	18	{	{	PUNCT
ma-51	322	19	xn}∞n=0	xn}∞n=0	VERB
ma-51	322	20	generated	generate	VERB
ma-51	322	21	by	by	ADP
ma-51	322	22	(	(	PUNCT
ma-51	322	23	3.33	3.33	NUM
ma-51	322	24	)	)	PUNCT
ma-51	322	25	weakly	weakly	ADJ
ma-51	322	26	and	and	CCONJ
ma-51	322	27	strongly	strongly	ADV
ma-51	322	28	converges	converge	VERB
ma-51	322	29	to	to	ADP
ma-51	322	30	the	the	DET
ma-51	322	31	fixed	fix	VERB
ma-51	322	32	point	point	NOUN
ma-51	322	33	of	of	ADP
ma-51	322	34	t	t	PROPN
ma-51	322	35	.	.	PUNCT
ma-51	323	1	corollary	corollary	ADJ
ma-51	323	2	3.4	3.4	NUM
ma-51	323	3	.	.	PUNCT
ma-51	324	1	let	let	VERB
ma-51	324	2	h	h	PRON
ma-51	324	3	be	be	AUX
ma-51	324	4	a	a	DET
ma-51	324	5	real	real	ADJ
ma-51	324	6	hilbert	hilbert	NOUN
ma-51	324	7	space	space	NOUN
ma-51	324	8	,	,	PUNCT
ma-51	324	9	k	k	PROPN
ma-51	324	10	a	a	DET
ma-51	324	11	nonempty	nonempty	ADV
ma-51	324	12	closed	close	VERB
ma-51	324	13	convex	convex	NOUN
ma-51	324	14	subset	subset	NOUN
ma-51	324	15	of	of	ADP
ma-51	324	16	h	h	PROPN
ma-51	324	17	and	and	CCONJ
ma-51	324	18	t	t	PROPN
ma-51	324	19	:	:	PUNCT
ma-51	325	1	k	k	X
ma-51	325	2	−→	−→	NOUN
ma-51	325	3	k	k	PROPN
ma-51	325	4	is	be	AUX
ma-51	325	5	demicontractive	demicontractive	ADJ
ma-51	325	6	mapping	mapping	NOUN
ma-51	325	7	.	.	PUNCT
ma-51	326	1	for	for	ADP
ma-51	326	2	any	any	DET
ma-51	326	3	arbitrary	arbitrary	ADJ
ma-51	326	4	x0	x0	PROPN
ma-51	326	5	∈	∈	PROPN
ma-51	326	6	h	h	NOUN
ma-51	326	7	,	,	PUNCT
ma-51	326	8	define	define	VERB
ma-51	326	9	the	the	DET
ma-51	326	10	sequence	sequence	NOUN
ma-51	326	11	{	{	PUNCT
ma-51	326	12	xn}∞n=0	xn}∞n=0	X
ma-51	326	13	iteratively	iteratively	ADV
ma-51	326	14	as	as	SCONJ
ma-51	326	15	follows	follow	VERB
ma-51	326	16	:	:	PUNCT
ma-51	326	17			PUNCT
ma-51	326	18	xn+1	xn+1	PROPN
ma-51	326	19	=	=	SYM
ma-51	326	20	pk	pk	X
ma-51	326	21	[	[	X
ma-51	326	22	(	(	PUNCT
ma-51	326	23	1−	1−	NUM
ma-51	326	24	αn	αn	NOUN
ma-51	326	25	−	−	PROPN
ma-51	326	26	γn)xn	γn)xn	PROPN
ma-51	326	27	+	+	CCONJ
ma-51	326	28	γntyn	γntyn	PROPN
ma-51	326	29	]	]	X
ma-51	326	30	yn	yn	PROPN
ma-51	326	31	=	=	SYM
ma-51	326	32	(	(	PUNCT
ma-51	326	33	1−	1−	NUM
ma-51	326	34	βn)xn	βn)xn	PROPN
ma-51	326	35	+	+	CCONJ
ma-51	326	36	βntxn	βntxn	ADJ
ma-51	326	37	,	,	PUNCT
ma-51	326	38	n	n	PRON
ma-51	326	39	≥	≥	NOUN
ma-51	326	40	1	1	NUM
ma-51	326	41	,	,	PUNCT
ma-51	326	42	(	(	PUNCT
ma-51	326	43	3.34	3.34	NUM
ma-51	326	44	)	)	PUNCT
ma-51	326	45	where	where	SCONJ
ma-51	326	46	the	the	DET
ma-51	326	47	sequences	sequence	NOUN
ma-51	326	48	{	{	PUNCT
ma-51	326	49	δn}∞n=0	δn}∞n=0	X
ma-51	326	50	,	,	PUNCT
ma-51	326	51	{	{	PUNCT
ma-51	326	52	γn}∞n=0	γn}∞n=0	VERB
ma-51	326	53	,	,	PUNCT
ma-51	326	54	{	{	PUNCT
ma-51	326	55	βn}∞n=0	βn}∞n=0	X
ma-51	326	56	∈	∈	PROPN
ma-51	326	57	(	(	PUNCT
ma-51	326	58	0	0	NUM
ma-51	326	59	,	,	PUNCT
ma-51	326	60	1	1	X
ma-51	326	61	)	)	PUNCT
ma-51	326	62	satisfy	satisfy	VERB
ma-51	326	63	the	the	DET
ma-51	326	64	following	follow	VERB
ma-51	326	65	conditions	condition	NOUN
ma-51	326	66	:	:	PUNCT
ma-51	326	67	(	(	PUNCT
ma-51	326	68	i	i	NOUN
ma-51	326	69	)	)	PUNCT
ma-51	326	70	0	0	PUNCT
ma-51	327	1	<	<	X
ma-51	327	2	δ	δ	PROPN
ma-51	327	3	≤	≤	NUM
ma-51	327	4	δn	δn	ADJ
ma-51	327	5	≤	≤	NUM
ma-51	327	6	βn	βn	NOUN
ma-51	327	7	≤	≤	NUM
ma-51	327	8	γn	γn	ADP
ma-51	327	9	≤	≤	NUM
ma-51	327	10	γ	γ	X
ma-51	327	11	≤	≤	NOUN
ma-51	327	12	1−	1−	NUM
ma-51	327	13	δ	δ	NOUN
ma-51	327	14	1	1	NUM
ma-51	327	15	+	+	CCONJ
ma-51	327	16	l2	l2	NOUN
ma-51	327	17	;	;	PUNCT
ma-51	327	18	(	(	PUNCT
ma-51	327	19	i	i	PRON
ma-51	327	20	i	i	PROPN
ma-51	327	21	)	)	PUNCT
ma-51	327	22	limn→∞	limn→∞	VERB
ma-51	327	23	δn	δn	NOUN
ma-51	327	24	=	=	SYM
ma-51	327	25	0	0	NUM
ma-51	327	26	and	and	CCONJ
ma-51	327	27	∑∞	∑∞	NOUN
ma-51	327	28	n=0	n=0	X
ma-51	327	29	δn	δn	NOUN
ma-51	327	30	=	=	PUNCT
ma-51	327	31	∞.	∞.	PROPN
ma-51	327	32	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	327	33	eur	eur	PROPN
ma-51	327	34	.	.	PUNCT
ma-51	328	1	j.	j.	PROPN
ma-51	328	2	math	math	PROPN
ma-51	328	3	.	.	PUNCT
ma-51	329	1	anal	anal	PROPN
ma-51	329	2	.	.	PUNCT
ma-51	330	1	10.28924	10.28924	NUM
ma-51	330	2	/	/	SYM
ma-51	330	3	ada	ada	PROPN
ma-51	330	4	/	/	SYM
ma-51	330	5	ma.2.10	ma.2.10	PROPN
ma-51	330	6	12	12	NUM
ma-51	330	7	then	then	ADV
ma-51	330	8	,	,	PUNCT
ma-51	330	9	the	the	DET
ma-51	330	10	sequence	sequence	NOUN
ma-51	330	11	{	{	PUNCT
ma-51	330	12	xn}∞n=0	xn}∞n=0	VERB
ma-51	330	13	generated	generate	VERB
ma-51	330	14	by	by	ADP
ma-51	330	15	(	(	PUNCT
ma-51	330	16	3.34	3.34	NUM
ma-51	330	17	)	)	PUNCT
ma-51	330	18	weakly	weakly	ADJ
ma-51	330	19	and	and	CCONJ
ma-51	330	20	strongly	strongly	ADV
ma-51	330	21	converges	converge	VERB
ma-51	330	22	to	to	ADP
ma-51	330	23	the	the	DET
ma-51	330	24	fixed	fix	VERB
ma-51	330	25	point	point	NOUN
ma-51	330	26	of	of	ADP
ma-51	330	27	t	t	PROPN
ma-51	330	28	.	.	PUNCT
ma-51	331	1	competing	compete	VERB
ma-51	331	2	interest	interest	NOUN
ma-51	331	3	.	.	PUNCT
ma-51	332	1	the	the	DET
ma-51	332	2	authors	author	NOUN
ma-51	332	3	declare	declare	VERB
ma-51	332	4	that	that	SCONJ
ma-51	332	5	there	there	PRON
ma-51	332	6	is	be	VERB
ma-51	332	7	no	no	DET
ma-51	332	8	conflict	conflict	NOUN
ma-51	332	9	of	of	ADP
ma-51	332	10	interest	interest	NOUN
ma-51	332	11	.	.	PUNCT
ma-51	333	1	references	reference	NOUN
ma-51	333	2	[	[	X
ma-51	333	3	1	1	NUM
ma-51	333	4	]	]	X
ma-51	333	5	f.e	f.e	PROPN
ma-51	333	6	.	.	PROPN
ma-51	333	7	browder	browder	PROPN
ma-51	333	8	,	,	PUNCT
ma-51	333	9	nonlinear	nonlinear	ADJ
ma-51	333	10	mappings	mapping	NOUN
ma-51	333	11	of	of	ADP
ma-51	333	12	nonexpansive	nonexpansive	ADJ
ma-51	333	13	and	and	CCONJ
ma-51	333	14	accretive	accretive	ADJ
ma-51	333	15	type	type	NOUN
ma-51	333	16	in	in	ADP
ma-51	333	17	banach	banach	NOUN
ma-51	333	18	spaces	space	NOUN
ma-51	333	19	,	,	PUNCT
ma-51	333	20	bull	bull	NOUN
ma-51	333	21	.	.	PUNCT
ma-51	334	1	amer	amer	PROPN
ma-51	334	2	.	.	PUNCT
ma-51	334	3	math	math	PROPN
ma-51	334	4	.	.	PUNCT
ma-51	335	1	soc.73	soc.73	NOUN
ma-51	335	2	(	(	PUNCT
ma-51	335	3	1967	1967	NUM
ma-51	335	4	)	)	PUNCT
ma-51	335	5	875	875	NUM
ma-51	335	6	-	-	SYM
ma-51	335	7	882.[2	882.[2	NUM
ma-51	335	8	]	]	X
ma-51	335	9	f.e	f.e	PROPN
ma-51	335	10	.	.	PROPN
ma-51	335	11	browder	browder	PROPN
ma-51	335	12	,	,	PUNCT
ma-51	335	13	w.v	w.v	PROPN
ma-51	335	14	.	.	PROPN
ma-51	335	15	petryshyn	petryshyn	PROPN
ma-51	335	16	,	,	PUNCT
ma-51	335	17	construction	construction	NOUN
ma-51	335	18	of	of	ADP
ma-51	335	19	fixed	fix	VERB
ma-51	335	20	points	point	NOUN
ma-51	335	21	of	of	ADP
ma-51	335	22	nonlinear	nonlinear	ADJ
ma-51	335	23	mappings	mapping	NOUN
ma-51	335	24	in	in	ADP
ma-51	335	25	hilbert	hilbert	PROPN
ma-51	335	26	space	space	NOUN
ma-51	335	27	,	,	PUNCT
ma-51	335	28	j.	j.	PROPN
ma-51	335	29	math	math	PROPN
ma-51	335	30	.	.	PUNCT
ma-51	336	1	anal.appl	anal.appl	PROPN
ma-51	336	2	.	.	PROPN
ma-51	336	3	20	20	NUM
ma-51	336	4	(	(	PUNCT
ma-51	336	5	1967	1967	NUM
ma-51	336	6	)	)	PUNCT
ma-51	336	7	197	197	NUM
ma-51	336	8	-	-	SYM
ma-51	336	9	228	228	NUM
ma-51	336	10	.	.	PUNCT
ma-51	337	1	https://doi.org/10.1016/0022-247x(67)90085-6.[3	https://doi.org/10.1016/0022-247x(67)90085-6.[3	PROPN
ma-51	337	2	]	]	X
ma-51	337	3	c.e	c.e	PROPN
ma-51	337	4	.	.	PROPN
ma-51	337	5	chidume	chidume	PROPN
ma-51	337	6	,	,	PUNCT
ma-51	337	7	picards	picard	NOUN
ma-51	337	8	iteration	iteration	NOUN
ma-51	337	9	for	for	ADP
ma-51	337	10	nonlinear	nonlinear	ADJ
ma-51	337	11	lipschitz	lipschitz	NOUN
ma-51	337	12	strong	strong	ADJ
ma-51	337	13	pseudocontractions	pseudocontraction	NOUN
ma-51	337	14	in	in	ADP
ma-51	337	15	uniformly	uniformly	ADV
ma-51	337	16	strong	strong	ADJ
ma-51	337	17	banachspaces	banachspace	NOUN
ma-51	337	18	,	,	PUNCT
ma-51	337	19	ictp	ictp	ADJ
ma-51	337	20	preprint	preprint	NOUN
ma-51	337	21	,	,	PUNCT
ma-51	337	22	ic/951	ic/951	NOUN
ma-51	337	23	,	,	PUNCT
ma-51	337	24	(	(	PUNCT
ma-51	337	25	1995	1995	NUM
ma-51	337	26	)	)	PUNCT
ma-51	337	27	88	88	NUM
ma-51	337	28	.	.	PUNCT
ma-51	338	1	https://www.osti.gov/etdeweb/biblio/194049.[4	https://www.osti.gov/etdeweb/biblio/194049.[4	PRON
ma-51	338	2	]	]	X
ma-51	338	3	c.e	c.e	PROPN
ma-51	338	4	.	.	PROPN
ma-51	338	5	chidume	chidume	PROPN
ma-51	338	6	,	,	PUNCT
ma-51	338	7	geometric	geometric	ADJ
ma-51	338	8	properties	property	NOUN
ma-51	338	9	of	of	ADP
ma-51	338	10	banach	banach	NOUN
ma-51	338	11	spaces	space	NOUN
ma-51	338	12	and	and	CCONJ
ma-51	338	13	nonlinear	nonlinear	ADJ
ma-51	338	14	iterations	iteration	NOUN
ma-51	338	15	,	,	PUNCT
ma-51	338	16	springer	springer	NOUN
ma-51	338	17	-	-	PUNCT
ma-51	338	18	verlag	verlag	PROPN
ma-51	338	19	,	,	PUNCT
ma-51	338	20	london	london	PROPN
ma-51	338	21	,	,	PUNCT
ma-51	338	22	(	(	PUNCT
ma-51	338	23	2009).[5	2009).[5	NUM
ma-51	338	24	]	]	X
ma-51	338	25	c.	c.	PROPN
ma-51	338	26	chidume	chidume	PROPN
ma-51	338	27	,	,	PUNCT
ma-51	338	28	c.	c.	PROPN
ma-51	338	29	moore	moore	PROPN
ma-51	338	30	,	,	PUNCT
ma-51	338	31	fixed	fix	VERB
ma-51	338	32	point	point	NOUN
ma-51	338	33	iteration	iteration	NOUN
ma-51	338	34	for	for	ADP
ma-51	338	35	pseudocontractive	pseudocontractive	ADJ
ma-51	338	36	maps	map	NOUN
ma-51	338	37	,	,	PUNCT
ma-51	338	38	proc	proc	PROPN
ma-51	338	39	.	.	PUNCT
ma-51	339	1	amer	amer	PROPN
ma-51	339	2	.	.	PUNCT
ma-51	339	3	math	math	PROPN
ma-51	339	4	.	.	PUNCT
ma-51	340	1	soc	soc	PROPN
ma-51	340	2	.	.	PUNCT
ma-51	341	1	127	127	NUM
ma-51	341	2	(	(	PUNCT
ma-51	341	3	1999	1999	NUM
ma-51	341	4	)	)	PUNCT
ma-51	341	5	1163	1163	NUM
ma-51	341	6	-	-	SYM
ma-51	341	7	1170	1170	NUM
ma-51	341	8	.	.	PUNCT
ma-51	342	1	https://doi.org/10.1090/s0002-9939-99-05050-9.[6	https://doi.org/10.1090/s0002-9939-99-05050-9.[6	PUNCT
ma-51	342	2	]	]	X
ma-51	343	1	c.e	c.e	PROPN
ma-51	343	2	.	.	PROPN
ma-51	343	3	chidume	chidume	PROPN
ma-51	343	4	,	,	PUNCT
ma-51	343	5	s.a	s.a	PROPN
ma-51	343	6	.	.	PROPN
ma-51	343	7	mutangadura	mutangadura	PROPN
ma-51	343	8	,	,	PUNCT
ma-51	343	9	an	an	DET
ma-51	343	10	example	example	NOUN
ma-51	343	11	of	of	ADP
ma-51	343	12	the	the	DET
ma-51	343	13	mann	mann	PROPN
ma-51	343	14	iterative	iterative	NOUN
ma-51	343	15	method	method	NOUN
ma-51	343	16	for	for	ADP
ma-51	343	17	lipschitz	lipschitz	NOUN
ma-51	343	18	pseudocontractions	pseudocontraction	NOUN
ma-51	343	19	,	,	PUNCT
ma-51	343	20	proc.amer	proc.amer	PROPN
ma-51	343	21	.	.	PUNCT
ma-51	344	1	math	math	NOUN
ma-51	344	2	.	.	PUNCT
ma-51	345	1	soc	soc	PROPN
ma-51	345	2	.	.	PUNCT
ma-51	346	1	13	13	NUM
ma-51	346	2	(	(	PUNCT
ma-51	346	3	1974	1974	NUM
ma-51	346	4	)	)	PUNCT
ma-51	346	5	2359	2359	NUM
ma-51	346	6	-	-	SYM
ma-51	346	7	2363.[7	2363.[7	NUM
ma-51	346	8	]	]	X
ma-51	346	9	t.l	t.l	PROPN
ma-51	346	10	.	.	PROPN
ma-51	346	11	hicks	hicks	PROPN
ma-51	346	12	,	,	PUNCT
ma-51	346	13	j.d	j.d	PROPN
ma-51	346	14	.	.	PROPN
ma-51	346	15	kubicek	kubicek	PROPN
ma-51	346	16	,	,	PUNCT
ma-51	346	17	on	on	ADP
ma-51	346	18	the	the	DET
ma-51	346	19	mann	mann	PROPN
ma-51	346	20	iteration	iteration	NOUN
ma-51	346	21	process	process	NOUN
ma-51	346	22	in	in	ADP
ma-51	346	23	a	a	DET
ma-51	346	24	hilbert	hilbert	NOUN
ma-51	346	25	space	space	NOUN
ma-51	346	26	,	,	PUNCT
ma-51	346	27	j.	j.	PROPN
ma-51	346	28	math	math	PROPN
ma-51	346	29	.	.	PUNCT
ma-51	347	1	anal	anal	PROPN
ma-51	347	2	.	.	PUNCT
ma-51	348	1	appl	appl	PROPN
ma-51	348	2	.	.	PROPN
ma-51	349	1	59	59	NUM
ma-51	349	2	(	(	PUNCT
ma-51	349	3	1977	1977	NUM
ma-51	349	4	)	)	PUNCT
ma-51	349	5	498	498	NUM
ma-51	349	6	-	-	SYM
ma-51	349	7	504	504	NUM
ma-51	349	8	.	.	PUNCT
ma-51	350	1	https://doi.org/10.1016/0022-247x(77)90076-2.[8	https://doi.org/10.1016/0022-247x(77)90076-2.[8	PROPN
ma-51	350	2	]	]	X
ma-51	350	3	n.	n.	PROPN
ma-51	350	4	hussain	hussain	PROPN
ma-51	350	5	,	,	PUNCT
ma-51	350	6	a.	a.	PROPN
ma-51	350	7	rafiq	rafiq	PROPN
ma-51	350	8	,	,	PUNCT
ma-51	350	9	m.s	m.s	PROPN
ma-51	350	10	.	.	PROPN
ma-51	350	11	kang	kang	PROPN
ma-51	350	12	,	,	PUNCT
ma-51	350	13	iteration	iteration	NOUN
ma-51	350	14	schemes	scheme	NOUN
ma-51	350	15	for	for	ADP
ma-51	350	16	two	two	NUM
ma-51	350	17	hemicontractive	hemicontractive	ADJ
ma-51	350	18	mappings	mapping	NOUN
ma-51	350	19	in	in	ADP
ma-51	350	20	arbitrary	arbitrary	ADJ
ma-51	350	21	banach	banach	NOUN
ma-51	350	22	spaces	space	NOUN
ma-51	350	23	,	,	PUNCT
ma-51	350	24	int	int	NOUN
ma-51	350	25	.	.	PUNCT
ma-51	351	1	j.	j.	PROPN
ma-51	351	2	math	math	PROPN
ma-51	351	3	.	.	PUNCT
ma-51	352	1	anal	anal	ADJ
ma-51	352	2	.	.	PUNCT
ma-51	353	1	7	7	NUM
ma-51	353	2	(	(	PUNCT
ma-51	353	3	2013	2013	NUM
ma-51	353	4	)	)	PUNCT
ma-51	353	5	863	863	NUM
ma-51	353	6	-	-	SYM
ma-51	353	7	871.[9	871.[9	NUM
ma-51	353	8	]	]	X
ma-51	353	9	d.i	d.i	PROPN
ma-51	353	10	.	.	PROPN
ma-51	353	11	igbokwe	igbokwe	PROPN
ma-51	353	12	,	,	PUNCT
ma-51	353	13	construction	construction	NOUN
ma-51	353	14	of	of	ADP
ma-51	353	15	fixed	fix	VERB
ma-51	353	16	points	point	NOUN
ma-51	353	17	of	of	ADP
ma-51	353	18	strictly	strictly	ADV
ma-51	353	19	pseudocontractive	pseudocontractive	ADJ
ma-51	353	20	mappings	mapping	NOUN
ma-51	353	21	of	of	ADP
ma-51	353	22	browder	browder	NOUN
ma-51	353	23	-	-	PUNCT
ma-51	353	24	petryshn	petryshn	NOUN
ma-51	353	25	-	-	PUNCT
ma-51	353	26	type	type	NOUN
ma-51	353	27	inarbitrary	inarbitrary	ADJ
ma-51	353	28	banach	banach	NOUN
ma-51	353	29	spaces	space	NOUN
ma-51	353	30	,	,	PUNCT
ma-51	353	31	j.	j.	PROPN
ma-51	353	32	fixed	fix	VERB
ma-51	353	33	point	point	PROPN
ma-51	353	34	theory	theory	NOUN
ma-51	353	35	appl	appl	NOUN
ma-51	353	36	.	.	PROPN
ma-51	353	37	4	4	NUM
ma-51	353	38	(	(	PUNCT
ma-51	353	39	2004	2004	NUM
ma-51	353	40	)	)	PUNCT
ma-51	353	41	137	137	NUM
ma-51	353	42	-	-	SYM
ma-51	353	43	147.[10	147.[10	NUM
ma-51	353	44	]	]	X
ma-51	353	45	e.e	e.e	PROPN
ma-51	353	46	.	.	PROPN
ma-51	353	47	epuke	epuke	PROPN
ma-51	353	48	,	,	PUNCT
ma-51	353	49	approximation	approximation	NOUN
ma-51	353	50	of	of	ADP
ma-51	353	51	fixed	fix	VERB
ma-51	353	52	points	point	NOUN
ma-51	353	53	and	and	CCONJ
ma-51	353	54	solutions	solution	NOUN
ma-51	353	55	of	of	ADP
ma-51	353	56	variational	variational	ADJ
ma-51	353	57	inequalities	inequality	NOUN
ma-51	353	58	for	for	ADP
ma-51	353	59	certain	certain	ADJ
ma-51	353	60	classes	class	NOUN
ma-51	353	61	of	of	ADP
ma-51	353	62	mappingsusing	mappingsuse	VERB
ma-51	353	63	hybrid	hybrid	ADJ
ma-51	353	64	iteration	iteration	NOUN
ma-51	353	65	scheme	scheme	NOUN
ma-51	353	66	,	,	PUNCT
ma-51	353	67	unpublished	unpublished	ADJ
ma-51	353	68	m.sc	m.sc	PROPN
ma-51	353	69	.	.	PUNCT
ma-51	354	1	thesis	thesis	NOUN
ma-51	354	2	,	,	PUNCT
ma-51	354	3	university	university	PROPN
ma-51	354	4	of	of	ADP
ma-51	354	5	nigeria	nigeria	PROPN
ma-51	354	6	,	,	PUNCT
ma-51	354	7	nsukka	nsukka	PROPN
ma-51	354	8	,	,	PUNCT
ma-51	354	9	(	(	PUNCT
ma-51	354	10	2010).[11	2010).[11	NUM
ma-51	354	11	]	]	X
ma-51	354	12	l.	l.	PROPN
ma-51	354	13	qihou	qihou	PROPN
ma-51	354	14	,	,	PUNCT
ma-51	354	15	on	on	ADP
ma-51	354	16	naimpally	naimpally	ADV
ma-51	354	17	and	and	CCONJ
ma-51	354	18	singh	singh	PROPN
ma-51	354	19	’s	’s	PART
ma-51	354	20	open	open	ADJ
ma-51	354	21	questions	question	NOUN
ma-51	354	22	,	,	PUNCT
ma-51	354	23	j.	j.	PROPN
ma-51	354	24	math	math	PROPN
ma-51	354	25	.	.	PUNCT
ma-51	355	1	anal	anal	PROPN
ma-51	355	2	.	.	PUNCT
ma-51	356	1	appl	appl	PROPN
ma-51	356	2	.	.	PROPN
ma-51	357	1	124	124	NUM
ma-51	357	2	(	(	PUNCT
ma-51	357	3	1987	1987	NUM
ma-51	357	4	)	)	PUNCT
ma-51	357	5	157	157	NUM
ma-51	357	6	-	-	SYM
ma-51	357	7	164	164	NUM
ma-51	357	8	.	.	PUNCT
ma-51	358	1	https://doi.org/	https://doi.org/	VERB
ma-51	358	2	10.1016/0022	10.1016/0022	NUM
ma-51	358	3	-	-	NOUN
ma-51	358	4	247x(87)90031	247x(87)90031	NUM
ma-51	358	5	-	-	PUNCT
ma-51	358	6	x.[12	x.[12	PROPN
ma-51	358	7	]	]	X
ma-51	358	8	g.	g.	PROPN
ma-51	358	9	marino	marino	PROPN
ma-51	358	10	,	,	PUNCT
ma-51	358	11	h.-k	h.-k	PROPN
ma-51	358	12	.	.	PUNCT
ma-51	359	1	xu	xu	INTJ
ma-51	359	2	,	,	PUNCT
ma-51	359	3	weak	weak	ADJ
ma-51	359	4	and	and	CCONJ
ma-51	359	5	strong	strong	ADJ
ma-51	359	6	convergence	convergence	NOUN
ma-51	359	7	theorems	theorem	NOUN
ma-51	359	8	for	for	ADP
ma-51	359	9	strict	strict	ADJ
ma-51	359	10	pseudo	pseudo	NOUN
ma-51	359	11	-	-	NOUN
ma-51	359	12	contractions	contraction	NOUN
ma-51	359	13	in	in	ADP
ma-51	359	14	hilbert	hilbert	PROPN
ma-51	359	15	spaces	space	NOUN
ma-51	359	16	,	,	PUNCT
ma-51	359	17	j.math	j.math	NOUN
ma-51	359	18	.	.	PUNCT
ma-51	360	1	anal	anal	PROPN
ma-51	360	2	.	.	PUNCT
ma-51	360	3	appl	appl	PROPN
ma-51	360	4	.	.	PROPN
ma-51	361	1	329	329	NUM
ma-51	361	2	(	(	PUNCT
ma-51	361	3	2007	2007	NUM
ma-51	361	4	)	)	PUNCT
ma-51	361	5	336	336	NUM
ma-51	361	6	-	-	SYM
ma-51	361	7	346	346	NUM
ma-51	361	8	.	.	PUNCT
ma-51	362	1	https://doi.org/10.1016/j.jmaa.2006.06.055.[13	https://doi.org/10.1016/j.jmaa.2006.06.055.[13	PROPN
ma-51	362	2	]	]	X
ma-51	362	3	l.	l.	PROPN
ma-51	362	4	maruster	maruster	PROPN
ma-51	362	5	,	,	PUNCT
ma-51	362	6	s.	s.	PROPN
ma-51	362	7	maruster	maruster	PROPN
ma-51	362	8	,	,	PUNCT
ma-51	362	9	strong	strong	ADJ
ma-51	362	10	convergence	convergence	NOUN
ma-51	362	11	of	of	ADP
ma-51	362	12	the	the	DET
ma-51	362	13	mann	mann	PROPN
ma-51	362	14	iteration	iteration	NOUN
ma-51	362	15	for	for	ADP
ma-51	362	16	α	α	NOUN
ma-51	362	17	-	-	PUNCT
ma-51	362	18	demicontractive	demicontractive	ADJ
ma-51	362	19	mappings	mapping	NOUN
ma-51	362	20	,	,	PUNCT
ma-51	362	21	math	math	NOUN
ma-51	362	22	.	.	PUNCT
ma-51	362	23	com	com	NOUN
ma-51	362	24	-	-	PUNCT
ma-51	362	25	puter	puter	NOUN
ma-51	362	26	model	model	NOUN
ma-51	362	27	.	.	PUNCT
ma-51	363	1	54	54	NUM
ma-51	363	2	(	(	PUNCT
ma-51	363	3	2011	2011	NUM
ma-51	363	4	)	)	PUNCT
ma-51	363	5	2486	2486	NUM
ma-51	363	6	-	-	SYM
ma-51	363	7	2492	2492	NUM
ma-51	363	8	.	.	PUNCT
ma-51	364	1	https://doi.org/10.1016/j.mcm.2011.06.006.[14	https://doi.org/10.1016/j.mcm.2011.06.006.[14	PROPN
ma-51	364	2	]	]	PUNCT
ma-51	364	3	m.a	m.a	PROPN
ma-51	364	4	.	.	PROPN
ma-51	364	5	noor	noor	PROPN
ma-51	364	6	,	,	PUNCT
ma-51	364	7	k.i	k.i	PROPN
ma-51	364	8	.	.	PUNCT
ma-51	365	1	noor	noor	PROPN
ma-51	365	2	,	,	PUNCT
ma-51	365	3	t.m	t.m	PROPN
ma-51	365	4	.	.	PROPN
ma-51	365	5	rassias	rassias	PROPN
ma-51	365	6	,	,	PUNCT
ma-51	365	7	some	some	DET
ma-51	365	8	aspects	aspect	NOUN
ma-51	365	9	of	of	ADP
ma-51	365	10	variational	variational	ADJ
ma-51	365	11	inequalities	inequality	NOUN
ma-51	365	12	,	,	PUNCT
ma-51	365	13	j.	j.	PROPN
ma-51	365	14	comput	comput	PROPN
ma-51	365	15	.	.	PUNCT
ma-51	366	1	appl	appl	PROPN
ma-51	366	2	.	.	PROPN
ma-51	366	3	math	math	NOUN
ma-51	366	4	.	.	PUNCT
ma-51	367	1	47	47	NUM
ma-51	367	2	(	(	PUNCT
ma-51	367	3	1993)285	1993)285	NUM
ma-51	367	4	-	-	SYM
ma-51	367	5	312	312	NUM
ma-51	367	6	.	.	PUNCT
ma-51	368	1	https://doi.org/10.1016/0377-0427(93)90058-j.[15	https://doi.org/10.1016/0377-0427(93)90058-j.[15	PROPN
ma-51	368	2	]	]	X
ma-51	368	3	m.o	m.o	PROPN
ma-51	368	4	.	.	PROPN
ma-51	368	5	osilike	osilike	ADJ
ma-51	368	6	,	,	PUNCT
ma-51	368	7	strong	strong	ADJ
ma-51	368	8	and	and	CCONJ
ma-51	368	9	weak	weak	ADJ
ma-51	368	10	convergence	convergence	NOUN
ma-51	368	11	of	of	ADP
ma-51	368	12	ishikawa	ishikawa	PROPN
ma-51	368	13	iteration	iteration	NOUN
ma-51	368	14	methods	method	NOUN
ma-51	368	15	for	for	ADP
ma-51	368	16	a	a	DET
ma-51	368	17	class	class	NOUN
ma-51	368	18	of	of	ADP
ma-51	368	19	nonlinear	nonlinear	ADJ
ma-51	368	20	equations	equation	NOUN
ma-51	368	21	,	,	PUNCT
ma-51	368	22	bull.korean	bull.korean	PROPN
ma-51	368	23	math	math	NOUN
ma-51	368	24	.	.	PUNCT
ma-51	369	1	soc	soc	PROPN
ma-51	369	2	.	.	PUNCT
ma-51	370	1	37	37	NUM
ma-51	370	2	(	(	PUNCT
ma-51	370	3	2000	2000	NUM
ma-51	370	4	)	)	PUNCT
ma-51	370	5	153	153	NUM
ma-51	370	6	-	-	SYM
ma-51	370	7	169.[16	169.[16	NUM
ma-51	370	8	]	]	X
ma-51	370	9	m.o	m.o	PROPN
ma-51	370	10	.	.	PROPN
ma-51	370	11	osilike	osilike	PROPN
ma-51	370	12	,	,	PUNCT
ma-51	370	13	f.o	f.o	PROPN
ma-51	370	14	.	.	PROPN
ma-51	370	15	isiogugu	isiogugu	PROPN
ma-51	370	16	,	,	PUNCT
ma-51	370	17	weak	weak	ADJ
ma-51	370	18	and	and	CCONJ
ma-51	370	19	strong	strong	ADJ
ma-51	370	20	convergence	convergence	NOUN
ma-51	370	21	theorems	theorem	NOUN
ma-51	370	22	for	for	ADP
ma-51	370	23	nonspreading	nonspreading	ADJ
ma-51	370	24	-	-	PUNCT
ma-51	370	25	type	type	NOUN
ma-51	370	26	mappings	mapping	NOUN
ma-51	370	27	in	in	ADP
ma-51	370	28	hilbertspaces	hilbertspace	NOUN
ma-51	370	29	,	,	PUNCT
ma-51	370	30	nonlinear	nonlinear	ADJ
ma-51	370	31	anal	anal	NOUN
ma-51	370	32	.	.	PUNCT
ma-51	370	33	:	:	PUNCT
ma-51	371	1	theory	theory	NOUN
ma-51	371	2	methods	method	NOUN
ma-51	371	3	appl	appl	PROPN
ma-51	371	4	.	.	PUNCT
ma-51	372	1	74	74	NUM
ma-51	372	2	(	(	PUNCT
ma-51	372	3	2011	2011	NUM
ma-51	372	4	)	)	PUNCT
ma-51	372	5	1814	1814	NUM
ma-51	372	6	-	-	SYM
ma-51	372	7	1822	1822	NUM
ma-51	372	8	.	.	PUNCT
ma-51	373	1	https://doi.org/10.1016/j.na.2010	https://doi.org/10.1016/j.na.2010	PROPN
ma-51	373	2	.	.	PUNCT
ma-51	374	1	10.054.[17	10.054.[17	NUM
ma-51	374	2	]	]	X
ma-51	374	3	m.o	m.o	PROPN
ma-51	374	4	.	.	PROPN
ma-51	374	5	osilike	osilike	PROPN
ma-51	374	6	,	,	PUNCT
ma-51	374	7	a.c	a.c	PROPN
ma-51	374	8	.	.	PROPN
ma-51	374	9	onah	onah	PROPN
ma-51	374	10	,	,	PUNCT
ma-51	374	11	strong	strong	ADJ
ma-51	374	12	convergence	convergence	NOUN
ma-51	374	13	of	of	ADP
ma-51	374	14	the	the	DET
ma-51	374	15	ishikawa	ishikawa	PROPN
ma-51	374	16	iteration	iteration	NOUN
ma-51	374	17	for	for	ADP
ma-51	374	18	lipschitz	lipschitz	NOUN
ma-51	374	19	α	α	PRON
ma-51	374	20	-	-	PUNCT
ma-51	374	21	hemicontractive	hemicontractive	ADJ
ma-51	374	22	map	map	NOUN
ma-51	374	23	-	-	PUNCT
ma-51	374	24	pings	ping	NOUN
ma-51	374	25	,	,	PUNCT
ma-51	374	26	ann	ann	PROPN
ma-51	374	27	.	.	PROPN
ma-51	374	28	west	west	PROPN
ma-51	374	29	univ	univ	PROPN
ma-51	374	30	.	.	PUNCT
ma-51	375	1	timisoara	timisoara	PROPN
ma-51	375	2	math	math	PROPN
ma-51	375	3	.	.	PUNCT
ma-51	376	1	computer	computer	PROPN
ma-51	376	2	sci	sci	PROPN
ma-51	376	3	.	.	PROPN
ma-51	377	1	53	53	NUM
ma-51	377	2	(	(	PUNCT
ma-51	377	3	2015	2015	NUM
ma-51	377	4	)	)	PUNCT
ma-51	377	5	151	151	NUM
ma-51	377	6	-	-	SYM
ma-51	377	7	161	161	NUM
ma-51	377	8	.	.	PUNCT
ma-51	378	1	https://doi.org/10.1515/	https://doi.org/10.1515/	PROPN
ma-51	378	2	awutm-2015	awutm-2015	NOUN
ma-51	378	3	-	-	PUNCT
ma-51	378	4	0008.[18	0008.[18	NUM
ma-51	378	5	]	]	PUNCT
ma-51	378	6	l.	l.	PROPN
ma-51	378	7	wang	wang	PROPN
ma-51	378	8	,	,	PUNCT
ma-51	378	9	an	an	DET
ma-51	378	10	iteration	iteration	NOUN
ma-51	378	11	method	method	NOUN
ma-51	378	12	for	for	ADP
ma-51	378	13	nonexpansive	nonexpansive	ADJ
ma-51	378	14	mappings	mapping	NOUN
ma-51	378	15	in	in	ADP
ma-51	378	16	hilbert	hilbert	NOUN
ma-51	378	17	spaces	space	NOUN
ma-51	378	18	,	,	PUNCT
ma-51	378	19	fixed	fix	VERB
ma-51	378	20	point	point	NOUN
ma-51	378	21	theory	theory	NOUN
ma-51	378	22	appl	appl	PROPN
ma-51	378	23	.	.	PUNCT
ma-51	379	1	2007	2007	NUM
ma-51	379	2	(	(	PUNCT
ma-51	379	3	2007)28619	2007)28619	NUM
ma-51	379	4	.	.	PUNCT
ma-51	380	1	https://doi.org/10.1155/2007/28619	https://doi.org/10.1155/2007/28619	PROPN
ma-51	380	2	.	.	PUNCT
ma-51	381	1	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	381	2	https://doi.org/10.1016/0022-247x(67)90085-6	https://doi.org/10.1016/0022-247x(67)90085-6	PROPN
ma-51	381	3	https://www.osti.gov/etdeweb/biblio/194049	https://www.osti.gov/etdeweb/biblio/194049	X
ma-51	381	4	https://doi.org/10.1090/s0002-9939-99-05050-9	https://doi.org/10.1090/s0002-9939-99-05050-9	NUM
ma-51	381	5	https://doi.org/10.1016/0022-247x(77)90076-2	https://doi.org/10.1016/0022-247x(77)90076-2	PROPN
ma-51	381	6	https://doi.org/10.1016/0022-247x(87)90031-x	https://doi.org/10.1016/0022-247x(87)90031-x	PROPN
ma-51	381	7	https://doi.org/10.1016/0022-247x(87)90031-x	https://doi.org/10.1016/0022-247x(87)90031-x	PROPN
ma-51	381	8	https://doi.org/10.1016/j.jmaa.2006.06.055	https://doi.org/10.1016/j.jmaa.2006.06.055	NOUN
ma-51	381	9	https://doi.org/10.1016/j.mcm.2011.06.006	https://doi.org/10.1016/j.mcm.2011.06.006	X
ma-51	381	10	https://doi.org/10.1016/0377-0427(93)90058-j	https://doi.org/10.1016/0377-0427(93)90058-j	PROPN
ma-51	381	11	https://doi.org/10.1016/j.na.2010.10.054	https://doi.org/10.1016/j.na.2010.10.054	PROPN
ma-51	381	12	https://doi.org/10.1016/j.na.2010.10.054	https://doi.org/10.1016/j.na.2010.10.054	PROPN
ma-51	381	13	https://doi.org/10.1515/awutm-2015-0008	https://doi.org/10.1515/awutm-2015-0008	PROPN
ma-51	381	14	https://doi.org/10.1515/awutm-2015-0008	https://doi.org/10.1515/awutm-2015-0008	PROPN
ma-51	381	15	https://doi.org/10.1155/2007/28619	https://doi.org/10.1155/2007/28619	PROPN
ma-51	381	16	eur	eur	PROPN
ma-51	381	17	.	.	PUNCT
ma-51	382	1	j.	j.	PROPN
ma-51	382	2	math	math	PROPN
ma-51	382	3	.	.	PUNCT
ma-51	383	1	anal	anal	PROPN
ma-51	383	2	.	.	PUNCT
ma-51	384	1	10.28924	10.28924	NUM
ma-51	384	2	/	/	SYM
ma-51	384	3	ada	ada	PROPN
ma-51	384	4	/	/	SYM
ma-51	384	5	ma.2.10	ma.2.10	NOUN
ma-51	384	6	13	13	NUM
ma-51	384	7	[	[	SYM
ma-51	384	8	19	19	NUM
ma-51	384	9	]	]	X
ma-51	384	10	k.k	k.k	PROPN
ma-51	384	11	.	.	PROPN
ma-51	384	12	tan	tan	PROPN
ma-51	384	13	,	,	PUNCT
ma-51	384	14	h.k	h.k	PROPN
ma-51	384	15	.	.	PROPN
ma-51	384	16	xu	xu	PROPN
ma-51	384	17	,	,	PUNCT
ma-51	384	18	approximating	approximate	VERB
ma-51	384	19	fixed	fix	VERB
ma-51	384	20	points	point	NOUN
ma-51	384	21	of	of	ADP
ma-51	384	22	nonexpansive	nonexpansive	ADJ
ma-51	384	23	mappings	mapping	NOUN
ma-51	384	24	by	by	ADP
ma-51	384	25	the	the	DET
ma-51	384	26	ishikawa	ishikawa	PROPN
ma-51	384	27	iteration	iteration	NOUN
ma-51	384	28	process	process	NOUN
ma-51	384	29	,	,	PUNCT
ma-51	384	30	j.	j.	PROPN
ma-51	384	31	math.anal	math.anal	PROPN
ma-51	384	32	.	.	PUNCT
ma-51	384	33	appl	appl	PROPN
ma-51	384	34	.	.	PROPN
ma-51	384	35	178	178	NUM
ma-51	384	36	(	(	PUNCT
ma-51	384	37	1993	1993	NUM
ma-51	384	38	)	)	PUNCT
ma-51	384	39	301	301	NUM
ma-51	384	40	-	-	SYM
ma-51	384	41	308	308	NUM
ma-51	384	42	.	.	PUNCT
ma-51	385	1	https://doi.org/10.1006/jmaa.1993.1309.[20	https://doi.org/10.1006/jmaa.1993.1309.[20	NOUN
ma-51	385	2	]	]	PUNCT
ma-51	386	1	y.	y.	PROPN
ma-51	386	2	yao	yao	PROPN
ma-51	386	3	,	,	PUNCT
ma-51	386	4	y.-c	y.-c	PROPN
ma-51	386	5	.	.	PUNCT
ma-51	386	6	liou	liou	PROPN
ma-51	386	7	,	,	PUNCT
ma-51	386	8	g.	g.	PROPN
ma-51	386	9	marino	marino	PROPN
ma-51	386	10	,	,	PUNCT
ma-51	386	11	a	a	DET
ma-51	386	12	hybrid	hybrid	ADJ
ma-51	386	13	algorithm	algorithm	NOUN
ma-51	386	14	for	for	ADP
ma-51	386	15	pseudo	pseudo	NOUN
ma-51	386	16	-	-	ADJ
ma-51	386	17	contractive	contractive	ADJ
ma-51	386	18	mappings	mapping	NOUN
ma-51	386	19	,	,	PUNCT
ma-51	386	20	nonlinear	nonlinear	ADJ
ma-51	386	21	anal	anal	NOUN
ma-51	386	22	.	.	PUNCT
ma-51	386	23	:	:	PUNCT
ma-51	387	1	theory	theory	NOUN
ma-51	387	2	methodsappl	methodsappl	NOUN
ma-51	387	3	.	.	PUNCT
ma-51	388	1	71	71	NUM
ma-51	388	2	(	(	PUNCT
ma-51	388	3	2009	2009	NUM
ma-51	388	4	)	)	PUNCT
ma-51	388	5	4997	4997	NUM
ma-51	388	6	-	-	SYM
ma-51	388	7	5002	5002	NUM
ma-51	388	8	.	.	PUNCT
ma-51	389	1	https://doi.org/10.1016/j.na.2009.03.075.[21	https://doi.org/10.1016/j.na.2009.03.075.[21	PROPN
ma-51	389	2	]	]	PUNCT
ma-51	389	3	h.	h.	PROPN
ma-51	389	4	zhou	zhou	PROPN
ma-51	389	5	,	,	PUNCT
ma-51	389	6	convergence	convergence	NOUN
ma-51	389	7	theorems	theorem	NOUN
ma-51	389	8	of	of	ADP
ma-51	389	9	fixed	fix	VERB
ma-51	389	10	points	point	NOUN
ma-51	389	11	for	for	ADP
ma-51	389	12	lipschitz	lipschitz	VERB
ma-51	389	13	pseudo	pseudo	NOUN
ma-51	389	14	-	-	NOUN
ma-51	389	15	contractions	contraction	NOUN
ma-51	389	16	in	in	ADP
ma-51	389	17	hilbert	hilbert	PROPN
ma-51	389	18	spaces	space	NOUN
ma-51	389	19	,	,	PUNCT
ma-51	389	20	j.	j.	PROPN
ma-51	389	21	math	math	PROPN
ma-51	389	22	.	.	PUNCT
ma-51	390	1	anal.appl	anal.appl	PROPN
ma-51	390	2	.	.	PROPN
ma-51	391	1	343	343	NUM
ma-51	391	2	(	(	PUNCT
ma-51	391	3	2008	2008	NUM
ma-51	391	4	)	)	PUNCT
ma-51	391	5	546	546	NUM
ma-51	391	6	-	-	SYM
ma-51	391	7	556	556	NUM
ma-51	391	8	.	.	PUNCT
ma-51	392	1	https://doi.org/10.1016/j.jmaa.2008.01.045.[22	https://doi.org/10.1016/j.jmaa.2008.01.045.[22	NOUN
ma-51	392	2	]	]	X
ma-51	392	3	h.	h.	PROPN
ma-51	392	4	zhou	zhou	PROPN
ma-51	392	5	,	,	PUNCT
ma-51	392	6	demiclosedness	demiclosedness	NOUN
ma-51	392	7	principle	principle	NOUN
ma-51	392	8	with	with	ADP
ma-51	392	9	applications	application	NOUN
ma-51	392	10	for	for	ADP
ma-51	392	11	asymptotically	asymptotically	ADV
ma-51	392	12	pseudo	pseudo	NOUN
ma-51	392	13	-	-	NOUN
ma-51	392	14	contractions	contraction	NOUN
ma-51	392	15	in	in	ADP
ma-51	392	16	hilbert	hilbert	PROPN
ma-51	392	17	spaces	space	NOUN
ma-51	392	18	,	,	PUNCT
ma-51	392	19	nonlinear	nonlinear	ADJ
ma-51	392	20	anal	anal	NOUN
ma-51	392	21	.	.	PUNCT
ma-51	392	22	:	:	PUNCT
ma-51	392	23	theory	theory	NOUN
ma-51	392	24	methods	method	NOUN
ma-51	392	25	appl	appl	PROPN
ma-51	392	26	.	.	PUNCT
ma-51	393	1	70	70	NUM
ma-51	393	2	(	(	PUNCT
ma-51	393	3	2009	2009	NUM
ma-51	393	4	)	)	PUNCT
ma-51	393	5	3140	3140	NUM
ma-51	393	6	-	-	SYM
ma-51	393	7	3145	3145	NUM
ma-51	393	8	.	.	PUNCT
ma-51	394	1	https://doi.org/10.1016/j.na.2008.04.017.[23	https://doi.org/10.1016/j.na.2008.04.017.[23	PROPN
ma-51	394	2	]	]	PUNCT
ma-51	394	3	a.b	a.b	PROPN
ma-51	394	4	.	.	PROPN
ma-51	394	5	george	george	PROPN
ma-51	394	6	,	,	PUNCT
ma-51	394	7	weak	weak	ADJ
ma-51	394	8	and	and	CCONJ
ma-51	394	9	strong	strong	ADJ
ma-51	394	10	convergence	convergence	NOUN
ma-51	394	11	of	of	ADP
ma-51	394	12	the	the	DET
ma-51	394	13	ishikawa	ishikawa	PROPN
ma-51	394	14	iterative	iterative	NOUN
ma-51	394	15	sequence	sequence	NOUN
ma-51	394	16	to	to	ADP
ma-51	394	17	fixed	fix	VERB
ma-51	394	18	points	point	NOUN
ma-51	394	19	of	of	ADP
ma-51	394	20	lipschitz	lipschitz	VERB
ma-51	394	21	pseudo	pseudo	NOUN
ma-51	394	22	-	-	ADJ
ma-51	394	23	contractive	contractive	ADJ
ma-51	394	24	maps	map	NOUN
ma-51	394	25	in	in	ADP
ma-51	394	26	hilbert	hilbert	PROPN
ma-51	394	27	spaces	space	NOUN
ma-51	394	28	,	,	PUNCT
ma-51	394	29	adv	adv	PROPN
ma-51	394	30	.	.	PUNCT
ma-51	394	31	fixed	fix	VERB
ma-51	394	32	point	point	NOUN
ma-51	394	33	theory	theory	NOUN
ma-51	394	34	,	,	PUNCT
ma-51	394	35	5	5	NUM
ma-51	394	36	(	(	PUNCT
ma-51	394	37	2015	2015	NUM
ma-51	394	38	)	)	PUNCT
ma-51	394	39	147	147	NUM
ma-51	394	40	-	-	SYM
ma-51	394	41	157.[24	157.[24	PROPN
ma-51	394	42	]	]	X
ma-51	394	43	e.i	e.i	PROPN
ma-51	394	44	.	.	PROPN
ma-51	395	1	veluhan	veluhan	ADJ
ma-51	395	2	,	,	PUNCT
ma-51	395	3	weak	weak	ADJ
ma-51	395	4	and	and	CCONJ
ma-51	395	5	strong	strong	ADJ
ma-51	395	6	convergence	convergence	NOUN
ma-51	395	7	algorithm	algorithm	NOUN
ma-51	395	8	for	for	ADP
ma-51	395	9	lipschitz	lipschitz	NOUN
ma-51	395	10	pseudocontractive	pseudocontractive	ADJ
ma-51	395	11	maps	map	NOUN
ma-51	395	12	in	in	ADP
ma-51	395	13	hilbert	hilbert	PROPN
ma-51	395	14	spaces	space	NOUN
ma-51	395	15	,	,	PUNCT
ma-51	395	16	unpublished	unpublished	ADJ
ma-51	395	17	m.sc	m.sc	PROPN
ma-51	395	18	.	.	PUNCT
ma-51	396	1	thesis	thesis	NOUN
ma-51	396	2	,	,	PUNCT
ma-51	396	3	department	department	NOUN
ma-51	396	4	of	of	ADP
ma-51	396	5	mathematics	mathematics	PROPN
ma-51	396	6	,	,	PUNCT
ma-51	396	7	university	university	PROPN
ma-51	396	8	of	of	ADP
ma-51	396	9	nigeria	nigeria	PROPN
ma-51	396	10	,	,	PUNCT
ma-51	396	11	nsukka	nsukka	PROPN
ma-51	396	12	,	,	PUNCT
ma-51	396	13	(	(	PUNCT
ma-51	396	14	2014).[25	2014).[25	X
ma-51	396	15	]	]	X
ma-51	396	16	o.o	o.o	PROPN
ma-51	396	17	.	.	PROPN
ma-51	396	18	owojori	owojori	PROPN
ma-51	396	19	,	,	PUNCT
ma-51	396	20	some	some	DET
ma-51	396	21	convergence	convergence	NOUN
ma-51	396	22	results	result	VERB
ma-51	396	23	for	for	ADP
ma-51	396	24	fixed	fix	VERB
ma-51	396	25	point	point	NOUN
ma-51	396	26	of	of	ADP
ma-51	396	27	hemicontractive	hemicontractive	ADJ
ma-51	396	28	operators	operator	NOUN
ma-51	396	29	in	in	ADP
ma-51	396	30	some	some	DET
ma-51	396	31	banach	banach	NOUN
ma-51	396	32	spaces	space	NOUN
ma-51	396	33	,	,	PUNCT
ma-51	396	34	kragujevac	kragujevac	PROPN
ma-51	396	35	j.	j.	PROPN
ma-51	396	36	math	math	PROPN
ma-51	396	37	.	.	PUNCT
ma-51	397	1	31	31	NUM
ma-51	397	2	(	(	PUNCT
ma-51	397	3	2008	2008	NUM
ma-51	397	4	)	)	PUNCT
ma-51	397	5	111	111	NUM
ma-51	397	6	-	-	SYM
ma-51	397	7	129.[26	129.[26	NUM
ma-51	397	8	]	]	X
ma-51	397	9	c.	c.	PROPN
ma-51	397	10	morales	morales	PROPN
ma-51	397	11	,	,	PUNCT
ma-51	397	12	j.	j.	PROPN
ma-51	397	13	jung	jung	PROPN
ma-51	397	14	,	,	PUNCT
ma-51	397	15	convergence	convergence	NOUN
ma-51	397	16	of	of	ADP
ma-51	397	17	paths	path	NOUN
ma-51	397	18	for	for	ADP
ma-51	397	19	pseudo	pseudo	NOUN
ma-51	397	20	-	-	ADJ
ma-51	397	21	contractive	contractive	ADJ
ma-51	397	22	mappings	mapping	NOUN
ma-51	397	23	in	in	ADP
ma-51	397	24	banach	banach	NOUN
ma-51	397	25	spaces	space	NOUN
ma-51	397	26	,	,	PUNCT
ma-51	397	27	proc	proc	NOUN
ma-51	397	28	.	.	PUNCT
ma-51	398	1	amer	amer	PROPN
ma-51	398	2	.	.	PUNCT
ma-51	399	1	math.soc	math.soc	X
ma-51	399	2	.	.	PROPN
ma-51	399	3	128	128	NUM
ma-51	399	4	(	(	PUNCT
ma-51	399	5	2000	2000	NUM
ma-51	399	6	)	)	PUNCT
ma-51	399	7	3411	3411	NUM
ma-51	399	8	-	-	SYM
ma-51	399	9	3419	3419	NUM
ma-51	399	10	.	.	PUNCT
ma-51	400	1	https://doi.org/10.1090/s0002-9939-00-05573-8.[27	https://doi.org/10.1090/s0002-9939-00-05573-8.[27	PROPN
ma-51	400	2	]	]	PUNCT
ma-51	400	3	i.	i.	PROPN
ma-51	400	4	k.	k.	PROPN
ma-51	400	5	agwu	agwu	PROPN
ma-51	400	6	,	,	PUNCT
ma-51	400	7	d.	d.	PROPN
ma-51	400	8	i.	i.	PROPN
ma-51	400	9	igbokwe	igbokwe	PROPN
ma-51	400	10	,	,	PUNCT
ma-51	400	11	hybrid	hybrid	NOUN
ma-51	400	12	-	-	PUNCT
ma-51	400	13	type	type	NOUN
ma-51	400	14	iteration	iteration	NOUN
ma-51	400	15	scheme	scheme	NOUN
ma-51	400	16	for	for	ADP
ma-51	400	17	approximating	approximate	VERB
ma-51	400	18	fixed	fix	VERB
ma-51	400	19	point	point	NOUN
ma-51	400	20	of	of	ADP
ma-51	400	21	lipschitz	lipschitz	NOUN
ma-51	400	22	α	α	NOUN
ma-51	400	23	-	-	NOUN
ma-51	400	24	hemicontractivemappings	hemicontractivemapping	NOUN
ma-51	400	25	,	,	PUNCT
ma-51	400	26	adv	adv	PROPN
ma-51	400	27	.	.	PUNCT
ma-51	400	28	fixed	fix	VERB
ma-51	400	29	point	point	NOUN
ma-51	400	30	theory	theory	NOUN
ma-51	400	31	,	,	PUNCT
ma-51	400	32	10	10	NUM
ma-51	400	33	(	(	PUNCT
ma-51	400	34	2020	2020	NUM
ma-51	400	35	)	)	PUNCT
ma-51	400	36	3	3	NUM
ma-51	400	37	.	.	PUNCT
ma-51	401	1	https://doi.org/10.28919/afpt/4442	https://doi.org/10.28919/afpt/4442	PROPN
ma-51	401	2	.	.	PUNCT
ma-51	402	1	https://doi.org/10.28924/ada/ma.2.10	https://doi.org/10.28924/ada/ma.2.10	PROPN
ma-51	402	2	https://doi.org/10.1006/jmaa.1993.1309	https://doi.org/10.1006/jmaa.1993.1309	PROPN
ma-51	402	3	https://doi.org/10.1016/j.na.2009.03.075	https://doi.org/10.1016/j.na.2009.03.075	VERB
ma-51	402	4	https://doi.org/10.1016/j.jmaa.2008.01.045	https://doi.org/10.1016/j.jmaa.2008.01.045	ADJ
ma-51	402	5	https://doi.org/10.1016/j.na.2008.04.017	https://doi.org/10.1016/j.na.2008.04.017	NOUN
ma-51	402	6	https://doi.org/10.1090/s0002-9939-00-05573-8	https://doi.org/10.1090/s0002-9939-00-05573-8	NOUN
ma-51	402	7	https://doi.org/10.28919/afpt/4442	https://doi.org/10.28919/afpt/4442	PROPN
ma-51	402	8	1	1	NUM
ma-51	402	9	.	.	PUNCT
ma-51	403	1	introduction	introduction	NOUN
ma-51	403	2	2	2	NUM
ma-51	403	3	.	.	PUNCT
ma-51	403	4	preliminary	preliminary	ADJ
ma-51	403	5	3	3	NUM
ma-51	403	6	.	.	PUNCT
ma-51	403	7	convergence	convergence	NOUN
ma-51	403	8	results	result	VERB
ma-51	403	9	competing	compete	VERB
ma-51	403	10	interest	interest	NOUN
ma-51	403	11	references	reference	NOUN