id	sid	tid	token	lemma	pos
ma-154	1	1	2023	2023	NUM
ma-154	1	2	ada	ada	PROPN
ma-154	1	3	academica	academica	PROPN
ma-154	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-154	1	5	.	.	PUNCT
ma-154	2	1	j.	j.	PROPN
ma-154	2	2	math	math	PROPN
ma-154	2	3	.	.	PUNCT
ma-154	3	1	anal	anal	ADJ
ma-154	3	2	.	.	PUNCT
ma-154	4	1	3	3	NUM
ma-154	4	2	(	(	PUNCT
ma-154	4	3	2023	2023	NUM
ma-154	4	4	)	)	PUNCT
ma-154	4	5	15doi	15doi	NOUN
ma-154	4	6	:	:	PUNCT
ma-154	4	7	10.28924	10.28924	NUM
ma-154	4	8	/	/	SYM
ma-154	4	9	ada	ada	PROPN
ma-154	4	10	/	/	SYM
ma-154	4	11	ma.3.15	ma.3.15	NOUN
ma-154	4	12	developments	development	NOUN
ma-154	4	13	on	on	ADP
ma-154	4	14	the	the	DET
ma-154	4	15	convergence	convergence	NOUN
ma-154	4	16	analysis	analysis	NOUN
ma-154	4	17	of	of	ADP
ma-154	4	18	newton	newton	PROPN
ma-154	4	19	-	-	PUNCT
ma-154	4	20	kantorovich	kantorovich	PROPN
ma-154	4	21	method	method	NOUN
ma-154	4	22	for	for	ADP
ma-154	4	23	solving	solve	VERB
ma-154	4	24	nonlinear	nonlinear	ADJ
ma-154	4	25	equations	equation	NOUN
ma-154	4	26	samundra	samundra	VERB
ma-154	4	27	regmi1	regmi1	PROPN
ma-154	4	28	,	,	PUNCT
ma-154	4	29	ioannis	ioannis	PROPN
ma-154	4	30	k.	k.	PROPN
ma-154	4	31	argyros2,∗	argyros2,∗	PROPN
ma-154	4	32	,	,	PUNCT
ma-154	4	33	santhosh	santhosh	PROPN
ma-154	4	34	george3	george3	PROPN
ma-154	4	35	,	,	PUNCT
ma-154	4	36	michael	michael	PROPN
ma-154	4	37	i.	i.	PROPN
ma-154	4	38	argyros4	argyros4	PROPN
ma-154	5	1	1department	1department	NUM
ma-154	5	2	of	of	ADP
ma-154	5	3	mathematics	mathematic	NOUN
ma-154	5	4	,	,	PUNCT
ma-154	5	5	university	university	PROPN
ma-154	5	6	of	of	ADP
ma-154	5	7	houston	houston	PROPN
ma-154	5	8	,	,	PUNCT
ma-154	5	9	houston	houston	PROPN
ma-154	5	10	,	,	PUNCT
ma-154	5	11	tx	tx	PROPN
ma-154	5	12	77204	77204	NUM
ma-154	5	13	,	,	PUNCT
ma-154	5	14	usa	usa	PROPN
ma-154	5	15	sregmi5@uh.edu	sregmi5@uh.edu	PROPN
ma-154	5	16	2department	2department	NUM
ma-154	5	17	of	of	ADP
ma-154	5	18	computing	computing	NOUN
ma-154	5	19	and	and	CCONJ
ma-154	5	20	mathematical	mathematical	ADJ
ma-154	5	21	sciences	sciences	PROPN
ma-154	5	22	,	,	PUNCT
ma-154	5	23	cameron	cameron	PROPN
ma-154	5	24	university	university	PROPN
ma-154	5	25	,	,	PUNCT
ma-154	5	26	lawton	lawton	PROPN
ma-154	5	27	,	,	PUNCT
ma-154	5	28	ok	ok	PROPN
ma-154	5	29	73505	73505	NUM
ma-154	5	30	,	,	PUNCT
ma-154	5	31	usa	usa	PROPN
ma-154	5	32	iargyros@cameron.edu	iargyros@cameron.edu	PROPN
ma-154	6	1	3department	3department	NUM
ma-154	6	2	of	of	ADP
ma-154	6	3	mathematical	mathematical	ADJ
ma-154	6	4	and	and	CCONJ
ma-154	6	5	computational	computational	ADJ
ma-154	6	6	sciences	science	NOUN
ma-154	6	7	,	,	PUNCT
ma-154	6	8	national	national	PROPN
ma-154	6	9	institute	institute	PROPN
ma-154	6	10	of	of	ADP
ma-154	6	11	technology	technology	PROPN
ma-154	6	12	karnataka	karnataka	PROPN
ma-154	6	13	,	,	PUNCT
ma-154	6	14	india-575	india-575	ADJ
ma-154	6	15	025	025	NUM
ma-154	6	16	sgeorge@nitk.edu.in	sgeorge@nitk.edu.in	NOUN
ma-154	6	17	4department	4department	NUM
ma-154	6	18	of	of	ADP
ma-154	6	19	computer	computer	NOUN
ma-154	6	20	science	science	NOUN
ma-154	6	21	,	,	PUNCT
ma-154	6	22	university	university	PROPN
ma-154	6	23	of	of	ADP
ma-154	6	24	oklahoma	oklahoma	PROPN
ma-154	6	25	,	,	PUNCT
ma-154	6	26	norman	norman	PROPN
ma-154	6	27	,	,	PUNCT
ma-154	6	28	73019	73019	NUM
ma-154	6	29	,	,	PUNCT
ma-154	6	30	ok	ok	INTJ
ma-154	6	31	,	,	PUNCT
ma-154	6	32	usa	usa	PROPN
ma-154	6	33	michael.i.argyros-1@ou.edu	michael.i.argyros-1@ou.edu	PROPN
ma-154	6	34	∗correspondence	∗correspondence	NOUN
ma-154	6	35	:	:	PUNCT
ma-154	6	36	iargyros@cameron.edu	iargyros@cameron.edu	X
ma-154	6	37	abstract	abstract	ADJ
ma-154	6	38	.	.	PUNCT
ma-154	7	1	developments	development	NOUN
ma-154	7	2	are	be	AUX
ma-154	7	3	presented	present	VERB
ma-154	7	4	for	for	ADP
ma-154	7	5	the	the	DET
ma-154	7	6	semi	semi	ADJ
ma-154	7	7	-	-	ADJ
ma-154	7	8	local	local	ADJ
ma-154	7	9	convergence	convergence	NOUN
ma-154	7	10	of	of	ADP
ma-154	7	11	newton	newton	PROPN
ma-154	7	12	’s	’s	PART
ma-154	7	13	method	method	NOUN
ma-154	7	14	to	to	ADP
ma-154	7	15	solvebanach	solvebanach	PROPN
ma-154	7	16	space	space	NOUN
ma-154	7	17	-	-	PUNCT
ma-154	7	18	valued	value	VERB
ma-154	7	19	nonlinear	nonlinear	ADJ
ma-154	7	20	equations	equation	NOUN
ma-154	7	21	.	.	PUNCT
ma-154	8	1	by	by	ADP
ma-154	8	2	utilizing	utilize	VERB
ma-154	8	3	a	a	DET
ma-154	8	4	new	new	ADJ
ma-154	8	5	methodology	methodology	NOUN
ma-154	8	6	,	,	PUNCT
ma-154	8	7	we	we	PRON
ma-154	8	8	provide	provide	VERB
ma-154	8	9	a	a	DET
ma-154	8	10	finer	fine	ADJ
ma-154	8	11	con	con	NOUN
ma-154	8	12	-	-	PUNCT
ma-154	8	13	vergence	vergence	NOUN
ma-154	8	14	analysis	analysis	NOUN
ma-154	8	15	with	with	ADP
ma-154	8	16	no	no	DET
ma-154	8	17	additional	additional	ADJ
ma-154	8	18	conditions	condition	NOUN
ma-154	8	19	than	than	ADP
ma-154	8	20	in	in	ADP
ma-154	8	21	earlier	early	ADJ
ma-154	8	22	results	result	NOUN
ma-154	8	23	.	.	PUNCT
ma-154	9	1	in	in	ADP
ma-154	9	2	particular	particular	ADJ
ma-154	9	3	,	,	PUNCT
ma-154	9	4	this	this	PRON
ma-154	9	5	is	be	AUX
ma-154	9	6	done	do	VERB
ma-154	9	7	byintroducing	byintroduce	VERB
ma-154	9	8	the	the	DET
ma-154	9	9	center	center	ADJ
ma-154	9	10	-	-	PUNCT
ma-154	9	11	lipschitz	lipschitz	NOUN
ma-154	9	12	condition	condition	NOUN
ma-154	9	13	by	by	ADP
ma-154	9	14	which	which	PRON
ma-154	9	15	we	we	PRON
ma-154	9	16	construct	construct	VERB
ma-154	9	17	a	a	DET
ma-154	9	18	stricter	strict	ADJ
ma-154	9	19	domain	domain	NOUN
ma-154	9	20	than	than	ADP
ma-154	9	21	the	the	DET
ma-154	9	22	originaldomain	originaldomain	NOUN
ma-154	9	23	of	of	ADP
ma-154	9	24	the	the	DET
ma-154	9	25	operator	operator	NOUN
ma-154	9	26	.	.	PUNCT
ma-154	10	1	then	then	ADV
ma-154	10	2	,	,	PUNCT
ma-154	10	3	the	the	DET
ma-154	10	4	lipschitz	lipschitz	NOUN
ma-154	10	5	constants	constant	NOUN
ma-154	10	6	in	in	ADP
ma-154	10	7	the	the	DET
ma-154	10	8	new	new	ADJ
ma-154	10	9	domain	domain	NOUN
ma-154	10	10	are	be	AUX
ma-154	10	11	at	at	ADV
ma-154	10	12	least	least	ADJ
ma-154	10	13	as	as	ADP
ma-154	10	14	small	small	ADJ
ma-154	10	15	asthe	asthe	ADJ
ma-154	10	16	original	original	ADJ
ma-154	10	17	constants	constant	NOUN
ma-154	10	18	leading	lead	VERB
ma-154	10	19	to	to	ADP
ma-154	10	20	weaker	weak	ADJ
ma-154	10	21	sufficient	sufficient	ADJ
ma-154	10	22	convergence	convergence	NOUN
ma-154	10	23	criteria	criterion	NOUN
ma-154	10	24	,	,	PUNCT
ma-154	10	25	tighter	tight	ADJ
ma-154	10	26	error	error	NOUN
ma-154	10	27	bounds	bound	NOUN
ma-154	10	28	on	on	ADP
ma-154	10	29	theerror	theerror	ADJ
ma-154	10	30	distances	distance	NOUN
ma-154	10	31	involved	involve	VERB
ma-154	10	32	,	,	PUNCT
ma-154	10	33	and	and	CCONJ
ma-154	10	34	a	a	DET
ma-154	10	35	piece	piece	NOUN
ma-154	10	36	of	of	ADP
ma-154	10	37	better	well	ADJ
ma-154	10	38	information	information	NOUN
ma-154	10	39	on	on	ADP
ma-154	10	40	the	the	DET
ma-154	10	41	location	location	NOUN
ma-154	10	42	of	of	ADP
ma-154	10	43	the	the	DET
ma-154	10	44	solution	solution	NOUN
ma-154	10	45	.	.	PUNCT
ma-154	11	1	thesebenefits	thesebenefit	NOUN
ma-154	11	2	are	be	AUX
ma-154	11	3	obtained	obtain	VERB
ma-154	11	4	under	under	ADP
ma-154	11	5	the	the	DET
ma-154	11	6	same	same	ADJ
ma-154	11	7	computational	computational	ADJ
ma-154	11	8	cost	cost	NOUN
ma-154	11	9	since	since	SCONJ
ma-154	11	10	in	in	ADP
ma-154	11	11	practice	practice	NOUN
ma-154	11	12	the	the	DET
ma-154	11	13	computation	computation	NOUN
ma-154	11	14	of	of	ADP
ma-154	11	15	theoriginal	theoriginal	ADJ
ma-154	11	16	constants	constant	NOUN
ma-154	11	17	requires	require	VERB
ma-154	11	18	the	the	DET
ma-154	11	19	computation	computation	NOUN
ma-154	11	20	of	of	ADP
ma-154	11	21	the	the	DET
ma-154	11	22	new	new	ADJ
ma-154	11	23	constants	constant	NOUN
ma-154	11	24	as	as	ADP
ma-154	11	25	special	special	ADJ
ma-154	11	26	cases	case	NOUN
ma-154	11	27	.	.	PUNCT
ma-154	12	1	the	the	DET
ma-154	12	2	same	same	ADJ
ma-154	12	3	benefitsare	benefitsare	NOUN
ma-154	12	4	obtained	obtain	VERB
ma-154	12	5	if	if	SCONJ
ma-154	12	6	the	the	DET
ma-154	12	7	lipschitz	lipschitz	NOUN
ma-154	12	8	conditions	condition	NOUN
ma-154	12	9	are	be	AUX
ma-154	12	10	replaced	replace	VERB
ma-154	12	11	by	by	ADP
ma-154	12	12	hölder	hölder	NOUN
ma-154	12	13	conditions	condition	NOUN
ma-154	12	14	or	or	CCONJ
ma-154	12	15	even	even	ADV
ma-154	12	16	more	more	ADV
ma-154	12	17	general	general	ADJ
ma-154	12	18	ω−continuity	ω−continuity	NOUN
ma-154	12	19	conditions	condition	NOUN
ma-154	12	20	.	.	PUNCT
ma-154	13	1	this	this	DET
ma-154	13	2	methodology	methodology	NOUN
ma-154	13	3	can	can	AUX
ma-154	13	4	be	be	AUX
ma-154	13	5	applied	apply	VERB
ma-154	13	6	to	to	ADP
ma-154	13	7	other	other	ADJ
ma-154	13	8	methods	method	NOUN
ma-154	13	9	using	use	VERB
ma-154	13	10	such	such	ADJ
ma-154	13	11	as	as	ADP
ma-154	13	12	the	the	DET
ma-154	13	13	secant	secant	ADJ
ma-154	13	14	,	,	PUNCT
ma-154	13	15	stirling	stirling	PROPN
ma-154	13	16	’s	’s	PART
ma-154	13	17	newton	newton	PROPN
ma-154	13	18	-	-	PUNCT
ma-154	13	19	like	like	ADJ
ma-154	13	20	,	,	PUNCT
ma-154	13	21	and	and	CCONJ
ma-154	13	22	other	other	ADJ
ma-154	13	23	methods	method	NOUN
ma-154	13	24	along	along	ADP
ma-154	13	25	the	the	DET
ma-154	13	26	same	same	ADJ
ma-154	13	27	lines	line	NOUN
ma-154	13	28	.	.	PUNCT
ma-154	14	1	numerical	numerical	ADJ
ma-154	14	2	examples	example	NOUN
ma-154	14	3	indicate	indicate	VERB
ma-154	14	4	thatthe	thatthe	DET
ma-154	14	5	new	new	ADJ
ma-154	14	6	results	result	NOUN
ma-154	14	7	can	can	AUX
ma-154	14	8	be	be	AUX
ma-154	14	9	utilized	utilize	VERB
ma-154	14	10	to	to	PART
ma-154	14	11	solve	solve	VERB
ma-154	14	12	nonlinear	nonlinear	ADJ
ma-154	14	13	equations	equation	NOUN
ma-154	14	14	,	,	PUNCT
ma-154	14	15	but	but	CCONJ
ma-154	14	16	not	not	PART
ma-154	14	17	earlier	early	ADJ
ma-154	14	18	ones	one	NOUN
ma-154	14	19	.	.	PUNCT
ma-154	15	1	1	1	X
ma-154	15	2	.	.	X
ma-154	15	3	introduction	introduction	NOUN
ma-154	15	4	consider	consider	VERB
ma-154	15	5	the	the	DET
ma-154	15	6	problem	problem	NOUN
ma-154	15	7	of	of	ADP
ma-154	15	8	finding	find	VERB
ma-154	15	9	a	a	DET
ma-154	15	10	solution	solution	NOUN
ma-154	15	11	x∗	x∗	PROPN
ma-154	15	12	∈	∈	PROPN
ma-154	15	13	ω	ω	PROPN
ma-154	15	14	of	of	ADP
ma-154	15	15	the	the	DET
ma-154	15	16	equation	equation	NOUN
ma-154	15	17	f	f	X
ma-154	15	18	(	(	PUNCT
ma-154	15	19	x	x	X
ma-154	15	20	)	)	PUNCT
ma-154	15	21	=	=	SYM
ma-154	15	22	0	0	NUM
ma-154	15	23	,	,	PUNCT
ma-154	15	24	(	(	PUNCT
ma-154	15	25	1.1	1.1	NUM
ma-154	15	26	)	)	PUNCT
ma-154	15	27	received	receive	VERB
ma-154	15	28	:	:	PUNCT
ma-154	15	29	26	26	NUM
ma-154	15	30	jan	jan	PROPN
ma-154	15	31	2023	2023	NUM
ma-154	15	32	.	.	PUNCT
ma-154	16	1	key	key	ADJ
ma-154	16	2	words	word	NOUN
ma-154	16	3	and	and	CCONJ
ma-154	16	4	phrases	phrase	NOUN
ma-154	16	5	.	.	PUNCT
ma-154	17	1	newton	newton	PROPN
ma-154	17	2	-	-	PUNCT
ma-154	17	3	kantorovich	kantorovich	PROPN
ma-154	17	4	method	method	NOUN
ma-154	17	5	;	;	PUNCT
ma-154	17	6	convergence	convergence	NOUN
ma-154	17	7	;	;	PUNCT
ma-154	17	8	banach	banach	NOUN
ma-154	17	9	space.1	space.1	PROPN
ma-154	17	10	https://adac.ee	https://adac.ee	PROPN
ma-154	17	11	https://doi.org/10.28924/ada/ma.3.15	https://doi.org/10.28924/ada/ma.3.15	PROPN
ma-154	17	12	eur	eur	NOUN
ma-154	17	13	.	.	PUNCT
ma-154	18	1	j.	j.	PROPN
ma-154	18	2	math	math	PROPN
ma-154	18	3	.	.	PUNCT
ma-154	19	1	anal	anal	PROPN
ma-154	19	2	.	.	PUNCT
ma-154	20	1	10.28924	10.28924	NUM
ma-154	20	2	/	/	SYM
ma-154	20	3	ada	ada	PROPN
ma-154	20	4	/	/	SYM
ma-154	20	5	ma.3.15	ma.3.15	NOUN
ma-154	20	6	2where	2where	NUM
ma-154	20	7	f	f	X
ma-154	20	8	:	:	PUNCT
ma-154	20	9	ω	ω	NUM
ma-154	20	10	−→	−→	PROPN
ma-154	20	11	e2	e2	PROPN
ma-154	20	12	is	be	AUX
ma-154	20	13	a	a	DET
ma-154	20	14	continuously	continuously	ADV
ma-154	20	15	differentiable	differentiable	ADJ
ma-154	20	16	operator	operator	NOUN
ma-154	20	17	in	in	ADP
ma-154	20	18	the	the	DET
ma-154	20	19	fréchet	fréchet	ADJ
ma-154	20	20	-	-	PUNCT
ma-154	20	21	sense	sense	NOUN
ma-154	20	22	,	,	PUNCT
ma-154	20	23	e1	e1	PROPN
ma-154	20	24	,	,	PUNCT
ma-154	20	25	e2	e2	NOUN
ma-154	20	26	arebanach	arebanach	NOUN
ma-154	20	27	spaces	space	NOUN
ma-154	20	28	and	and	CCONJ
ma-154	20	29	ω	ω	NUM
ma-154	20	30	⊂	⊂	PROPN
ma-154	20	31	e1	e1	PROPN
ma-154	20	32	is	be	AUX
ma-154	20	33	an	an	DET
ma-154	20	34	open	open	ADJ
ma-154	20	35	set.the	set.the	DET
ma-154	20	36	solution	solution	NOUN
ma-154	20	37	x∗	x∗	PROPN
ma-154	20	38	in	in	ADP
ma-154	20	39	closed	closed	ADJ
ma-154	20	40	form	form	NOUN
ma-154	20	41	is	be	AUX
ma-154	20	42	desirable	desirable	ADJ
ma-154	20	43	.	.	PUNCT
ma-154	21	1	but	but	CCONJ
ma-154	21	2	this	this	PRON
ma-154	21	3	is	be	AUX
ma-154	21	4	possible	possible	ADJ
ma-154	21	5	only	only	ADV
ma-154	21	6	in	in	ADP
ma-154	21	7	special	special	ADJ
ma-154	21	8	cases	case	NOUN
ma-154	21	9	.	.	PUNCT
ma-154	22	1	so	so	ADV
ma-154	22	2	,	,	PUNCT
ma-154	22	3	most	most	ADJ
ma-154	22	4	solution	solution	NOUN
ma-154	22	5	methods	method	NOUN
ma-154	22	6	for	for	ADP
ma-154	22	7	(	(	PUNCT
ma-154	22	8	1.1	1.1	NUM
ma-154	22	9	)	)	PUNCT
ma-154	22	10	are	be	AUX
ma-154	22	11	iterative	iterative	ADJ
ma-154	22	12	methods	method	NOUN
ma-154	22	13	.	.	PUNCT
ma-154	23	1	the	the	DET
ma-154	23	2	convergence	convergence	NOUN
ma-154	23	3	regions	region	NOUN
ma-154	23	4	for	for	ADP
ma-154	23	5	these	these	DET
ma-154	23	6	methodsare	methodsare	NOUN
ma-154	23	7	small	small	ADJ
ma-154	23	8	in	in	ADP
ma-154	23	9	general	general	ADJ
ma-154	23	10	,	,	PUNCT
ma-154	23	11	so	so	ADV
ma-154	23	12	their	their	PRON
ma-154	23	13	applicability	applicability	NOUN
ma-154	23	14	is	be	AUX
ma-154	23	15	reduced	reduce	VERB
ma-154	23	16	.	.	PUNCT
ma-154	24	1	the	the	DET
ma-154	24	2	error	error	NOUN
ma-154	24	3	bounds	bound	NOUN
ma-154	24	4	are	be	AUX
ma-154	24	5	also	also	ADV
ma-154	24	6	pessimistic	pessimistic	ADJ
ma-154	24	7	(	(	PUNCT
ma-154	24	8	ingeneral).among	ingeneral).among	ADJ
ma-154	24	9	the	the	DET
ma-154	24	10	iterative	iterative	NOUN
ma-154	24	11	methods	method	NOUN
ma-154	24	12	,	,	PUNCT
ma-154	24	13	the	the	DET
ma-154	24	14	most	most	ADV
ma-154	24	15	famous	famous	ADJ
ma-154	24	16	one	one	NOUN
ma-154	24	17	is	be	AUX
ma-154	24	18	newton	newton	PROPN
ma-154	24	19	’s	’s	PART
ma-154	24	20	method	method	NOUN
ma-154	24	21	(	(	PUNCT
ma-154	24	22	nm	nm	NOUN
ma-154	24	23	)	)	PUNCT
ma-154	24	24	defined	define	VERB
ma-154	24	25	for	for	ADP
ma-154	24	26	n	n	NOUN
ma-154	24	27	=	=	SYM
ma-154	24	28	0	0	NUM
ma-154	24	29	,	,	PUNCT
ma-154	24	30	1	1	NUM
ma-154	24	31	,	,	PUNCT
ma-154	24	32	2	2	NUM
ma-154	24	33	,	,	PUNCT
ma-154	24	34	.	.	PUNCT
ma-154	24	35	.	.	PUNCT
ma-154	24	36	.	.	PUNCT
ma-154	25	1	by	by	ADP
ma-154	25	2	xn+1	xn+1	PROPN
ma-154	25	3	=	=	SYM
ma-154	25	4	xn	xn	PROPN
ma-154	26	1	−	−	PROPN
ma-154	26	2	f	f	PROPN
ma-154	26	3	′(xn)−1f	′(xn)−1f	PROPN
ma-154	26	4	(	(	PUNCT
ma-154	26	5	xn	xn	PROPN
ma-154	26	6	)	)	PUNCT
ma-154	26	7	(	(	PUNCT
ma-154	26	8	1.2)kantorovich	1.2)kantorovich	NUM
ma-154	26	9	provided	provide	VERB
ma-154	26	10	the	the	DET
ma-154	26	11	semi	semi	ADJ
ma-154	26	12	-	-	ADJ
ma-154	26	13	local	local	ADJ
ma-154	26	14	convergence	convergence	NOUN
ma-154	26	15	analysis	analysis	NOUN
ma-154	26	16	of	of	ADP
ma-154	26	17	nm	nm	NOUN
ma-154	26	18	utilizing	utilize	VERB
ma-154	26	19	the	the	DET
ma-154	26	20	contraction	contraction	NOUN
ma-154	26	21	map	map	NOUN
ma-154	26	22	-	-	PUNCT
ma-154	26	23	ping	ping	ADJ
ma-154	26	24	principle	principle	NOUN
ma-154	26	25	attributed	attribute	VERB
ma-154	26	26	to	to	ADP
ma-154	26	27	banach	banach	NOUN
ma-154	26	28	.	.	PUNCT
ma-154	27	1	in	in	ADP
ma-154	27	2	particular	particular	ADJ
ma-154	27	3	,	,	PUNCT
ma-154	27	4	he	he	PRON
ma-154	27	5	presented	present	VERB
ma-154	27	6	two	two	NUM
ma-154	27	7	different	different	ADJ
ma-154	27	8	proofs	proof	NOUN
ma-154	27	9	using	use	VERB
ma-154	27	10	majorantfunctions	majorantfunction	NOUN
ma-154	27	11	or	or	CCONJ
ma-154	27	12	recurrence	recurrence	NOUN
ma-154	27	13	relations	relation	NOUN
ma-154	27	14	[	[	X
ma-154	27	15	15	15	NUM
ma-154	27	16	]	]	PUNCT
ma-154	27	17	.	.	PUNCT
ma-154	28	1	his	his	PRON
ma-154	28	2	so	so	ADV
ma-154	28	3	-	-	PUNCT
ma-154	28	4	called	call	VERB
ma-154	28	5	newton	newton	PROPN
ma-154	28	6	-	-	PUNCT
ma-154	28	7	kantorovich	kantorovich	PROPN
ma-154	28	8	theorem	theorem	NOUN
ma-154	28	9	is	be	AUX
ma-154	28	10	that	that	SCONJ
ma-154	28	11	no	no	PRON
ma-154	28	12	as	as	SCONJ
ma-154	28	13	-	-	PUNCT
ma-154	28	14	sumption	sumption	NOUN
ma-154	28	15	on	on	ADP
ma-154	28	16	the	the	DET
ma-154	28	17	solution	solution	NOUN
ma-154	28	18	is	be	AUX
ma-154	28	19	made	make	VERB
ma-154	28	20	and	and	CCONJ
ma-154	28	21	at	at	ADP
ma-154	28	22	the	the	DET
ma-154	28	23	same	same	ADJ
ma-154	28	24	time	time	NOUN
ma-154	28	25	,	,	PUNCT
ma-154	28	26	the	the	DET
ma-154	28	27	existence	existence	NOUN
ma-154	28	28	of	of	ADP
ma-154	28	29	the	the	DET
ma-154	28	30	solution	solution	NOUN
ma-154	28	31	x∗	x∗	PRON
ma-154	28	32	is	be	AUX
ma-154	28	33	established.numerous	established.numerous	ADJ
ma-154	28	34	researchers	researcher	NOUN
ma-154	28	35	used	use	VERB
ma-154	28	36	this	this	DET
ma-154	28	37	theorem	theorem	NOUN
ma-154	28	38	in	in	ADP
ma-154	28	39	applications	application	NOUN
ma-154	28	40	and	and	CCONJ
ma-154	28	41	also	also	ADV
ma-154	28	42	as	as	ADP
ma-154	28	43	a	a	DET
ma-154	28	44	theoretical	theoretical	ADJ
ma-154	28	45	tool	tool	NOUN
ma-154	28	46	[	[	X
ma-154	28	47	1–16	1–16	NOUN
ma-154	28	48	]	]	PUNCT
ma-154	28	49	.	.	PUNCT
ma-154	29	1	butthe	butthe	PROPN
ma-154	29	2	convergence	convergence	NOUN
ma-154	29	3	criteria	criterion	NOUN
ma-154	29	4	may	may	AUX
ma-154	29	5	not	not	PART
ma-154	29	6	hold	hold	VERB
ma-154	29	7	although	although	SCONJ
ma-154	29	8	nm	nm	NOUN
ma-154	29	9	may	may	AUX
ma-154	29	10	converge	converge	VERB
ma-154	29	11	.	.	PUNCT
ma-154	30	1	motivated	motivate	VERB
ma-154	30	2	by	by	ADP
ma-154	30	3	these	these	DET
ma-154	30	4	concernsand	concernsand	NOUN
ma-154	30	5	optimization	optimization	NOUN
ma-154	30	6	considerations	consideration	NOUN
ma-154	30	7	we	we	PRON
ma-154	30	8	present	present	VERB
ma-154	30	9	new	new	ADJ
ma-154	30	10	results	result	NOUN
ma-154	30	11	that	that	PRON
ma-154	30	12	not	not	PART
ma-154	30	13	only	only	ADV
ma-154	30	14	extend	extend	VERB
ma-154	30	15	the	the	DET
ma-154	30	16	convergence	convergence	NOUN
ma-154	30	17	regionbut	regionbut	NOUN
ma-154	30	18	also	also	ADV
ma-154	30	19	provide	provide	VERB
ma-154	30	20	more	more	ADV
ma-154	30	21	precise	precise	ADJ
ma-154	30	22	error	error	NOUN
ma-154	30	23	estimates	estimate	NOUN
ma-154	30	24	and	and	CCONJ
ma-154	30	25	better	well	ADJ
ma-154	30	26	knowledge	knowledge	NOUN
ma-154	30	27	of	of	ADP
ma-154	30	28	the	the	DET
ma-154	30	29	location	location	NOUN
ma-154	30	30	of	of	ADP
ma-154	30	31	the	the	DET
ma-154	30	32	solution.the	solution.the	DET
ma-154	30	33	novelty	novelty	NOUN
ma-154	30	34	of	of	ADP
ma-154	30	35	the	the	DET
ma-154	30	36	article	article	NOUN
ma-154	30	37	is	be	AUX
ma-154	30	38	that	that	SCONJ
ma-154	30	39	these	these	DET
ma-154	30	40	benefits	benefit	NOUN
ma-154	30	41	require	require	VERB
ma-154	30	42	no	no	DET
ma-154	30	43	additional	additional	ADJ
ma-154	30	44	conditions	condition	NOUN
ma-154	30	45	.	.	PUNCT
ma-154	31	1	this	this	PRON
ma-154	31	2	is	be	AUX
ma-154	31	3	how	how	SCONJ
ma-154	31	4	theusage	theusage	NOUN
ma-154	31	5	of	of	ADP
ma-154	31	6	nm	nm	NOUN
ma-154	31	7	is	be	AUX
ma-154	31	8	extended	extend	VERB
ma-154	31	9	.	.	PUNCT
ma-154	32	1	the	the	DET
ma-154	32	2	technique	technique	NOUN
ma-154	32	3	used	use	VERB
ma-154	32	4	can	can	AUX
ma-154	32	5	be	be	AUX
ma-154	32	6	applied	apply	VERB
ma-154	32	7	to	to	PART
ma-154	32	8	extend	extend	VERB
ma-154	32	9	other	other	ADJ
ma-154	32	10	iterative	iterative	NOUN
ma-154	32	11	methodsalong	methodsalong	NOUN
ma-154	32	12	the	the	DET
ma-154	32	13	same	same	ADJ
ma-154	32	14	lines	line	NOUN
ma-154	32	15	.	.	PUNCT
ma-154	33	1	2	2	X
ma-154	33	2	.	.	X
ma-154	33	3	convergence	convergence	NOUN
ma-154	33	4	analysis	analysis	NOUN
ma-154	33	5	let	let	VERB
ma-154	33	6	α	α	PRON
ma-154	33	7	>	>	X
ma-154	33	8	0	0	PROPN
ma-154	33	9	,	,	PUNCT
ma-154	33	10	λ	λ	X
ma-154	33	11	≥	≥	NOUN
ma-154	33	12	0	0	NUM
ma-154	33	13	and	and	CCONJ
ma-154	33	14	x0	x0	PROPN
ma-154	33	15	∈	∈	PROPN
ma-154	33	16	ω	ω	NOUN
ma-154	33	17	be	be	AUX
ma-154	33	18	such	such	ADJ
ma-154	33	19	that	that	SCONJ
ma-154	33	20	‖f	‖f	PRON
ma-154	33	21	′(x0)−1‖	′(x0)−1‖	NOUN
ma-154	33	22	≤	≤	ADV
ma-154	33	23	α	α	X
ma-154	33	24	,	,	PUNCT
ma-154	33	25	‖f	‖f	ADJ
ma-154	33	26	′(x0)−1f	′(x0)−1f	NOUN
ma-154	33	27	(	(	PUNCT
ma-154	33	28	x0)‖	x0)‖	PROPN
ma-154	33	29	≤	≤	NUM
ma-154	33	30	λ	λ	PROPN
ma-154	33	31	and	and	CCONJ
ma-154	33	32	f	f	PROPN
ma-154	33	33	′(x0	′(x0	NOUN
ma-154	33	34	)	)	PUNCT
ma-154	34	1	−1	−1	NOUN
ma-154	34	2	∈	∈	PROPN
ma-154	34	3	l(e2	l(e2	NOUN
ma-154	34	4	,	,	PUNCT
ma-154	34	5	e1	e1	PROPN
ma-154	34	6	)	)	PUNCT
ma-154	34	7	,	,	PUNCT
ma-154	34	8	the	the	DET
ma-154	34	9	space	space	NOUN
ma-154	34	10	of	of	ADP
ma-154	34	11	bounded	bounded	ADJ
ma-154	34	12	linear	linear	PROPN
ma-154	34	13	operators	operator	NOUN
ma-154	34	14	from	from	ADP
ma-154	34	15	e2	e2	PROPN
ma-154	34	16	to	to	ADP
ma-154	34	17	e1	e1	PROPN
ma-154	34	18	.	.	PUNCT
ma-154	35	1	by	by	ADP
ma-154	35	2	b(x	b(x	NOUN
ma-154	35	3	,	,	PUNCT
ma-154	35	4	b	b	NOUN
ma-154	35	5	)	)	PUNCT
ma-154	35	6	,	,	PUNCT
ma-154	35	7	b[x	b[x	PROPN
ma-154	35	8	,	,	PUNCT
ma-154	35	9	b	b	NOUN
ma-154	35	10	]	]	X
ma-154	35	11	wedenote	wedenote	NOUN
ma-154	35	12	the	the	DET
ma-154	35	13	open	open	ADJ
ma-154	35	14	and	and	CCONJ
ma-154	35	15	closed	closed	ADJ
ma-154	35	16	balls	ball	NOUN
ma-154	35	17	in	in	ADP
ma-154	35	18	e1	e1	NOUN
ma-154	35	19	,	,	PUNCT
ma-154	35	20	respectively	respectively	ADV
ma-154	35	21	with	with	ADP
ma-154	35	22	center	center	NOUN
ma-154	35	23	x	x	SYM
ma-154	35	24	∈	∈	PROPN
ma-154	35	25	e1	e1	PROPN
ma-154	35	26	and	and	CCONJ
ma-154	35	27	of	of	ADP
ma-154	35	28	radius	radius	PROPN
ma-154	35	29	b	b	PROPN
ma-154	35	30	>	>	X
ma-154	35	31	0.some	0.some	NUM
ma-154	35	32	lipschitz	lipschitz	NOUN
ma-154	35	33	-	-	PUNCT
ma-154	35	34	type	type	NOUN
ma-154	35	35	conditions	condition	NOUN
ma-154	35	36	are	be	AUX
ma-154	35	37	needed	need	VERB
ma-154	35	38	.	.	PUNCT
ma-154	36	1	definition	definition	NOUN
ma-154	36	2	2.1	2.1	NUM
ma-154	36	3	.	.	PUNCT
ma-154	37	1	operator	operator	NOUN
ma-154	37	2	f	f	PROPN
ma-154	37	3	′	′	NOUN
ma-154	37	4	is	be	AUX
ma-154	37	5	center	center	ADJ
ma-154	37	6	-	-	PUNCT
ma-154	37	7	lipschitz	lipschitz	NOUN
ma-154	37	8	continuous	continuous	ADJ
ma-154	37	9	about	about	ADP
ma-154	37	10	x0	x0	PROPN
ma-154	37	11	on	on	ADP
ma-154	37	12	ω	ω	NUM
ma-154	37	13	if	if	SCONJ
ma-154	37	14	there	there	PRON
ma-154	37	15	exists	exist	VERB
ma-154	37	16	l0	l0	PROPN
ma-154	37	17	>	>	X
ma-154	37	18	0	0	NUM
ma-154	37	19	such	such	ADJ
ma-154	37	20	that	that	PRON
ma-154	37	21	for	for	ADP
ma-154	37	22	all	all	PRON
ma-154	37	23	u	u	PROPN
ma-154	37	24	∈	∈	PROPN
ma-154	37	25	ω	ω	NOUN
ma-154	37	26	‖f	‖f	SCONJ
ma-154	37	27	′(u)−	′(u)−	PROPN
ma-154	37	28	f	f	PROPN
ma-154	38	1	′(x0)‖	′(x0)‖	NOUN
ma-154	38	2	≤	≤	NUM
ma-154	38	3	l0‖u	l0‖u	NUM
ma-154	38	4	−	−	PROPN
ma-154	39	1	x0‖.	x0‖.	PROPN
ma-154	39	2	(	(	PUNCT
ma-154	39	3	2.1	2.1	NUM
ma-154	39	4	)	)	PUNCT
ma-154	39	5	set	set	VERB
ma-154	39	6	ω0	ω0	ADV
ma-154	39	7	=	=	SYM
ma-154	39	8	b(x0	b(x0	NOUN
ma-154	39	9	,	,	PUNCT
ma-154	39	10	1	1	NUM
ma-154	39	11	αl0	αl0	NOUN
ma-154	39	12	)	)	PUNCT
ma-154	40	1	∩ω	∩ω	INTJ
ma-154	40	2	.	.	PUNCT
ma-154	41	1	(	(	PUNCT
ma-154	41	2	2.2	2.2	NUM
ma-154	41	3	)	)	PUNCT
ma-154	41	4	definition	definition	NOUN
ma-154	41	5	2.2	2.2	NUM
ma-154	41	6	.	.	PUNCT
ma-154	42	1	operator	operator	NOUN
ma-154	42	2	f	f	PROPN
ma-154	42	3	′	′	PROPN
ma-154	42	4	is	be	AUX
ma-154	42	5	1−restricted	1−restricted	ADJ
ma-154	42	6	lipschitz	lipschitz	NOUN
ma-154	42	7	continuous	continuous	ADJ
ma-154	42	8	on	on	ADP
ma-154	42	9	ω0	ω0	NOUN
ma-154	42	10	if	if	SCONJ
ma-154	42	11	there	there	PRON
ma-154	42	12	exists	exist	VERB
ma-154	42	13	l	l	NOUN
ma-154	42	14	>	>	X
ma-154	42	15	0	0	NUM
ma-154	42	16	such	such	ADJ
ma-154	42	17	that	that	SCONJ
ma-154	42	18	‖f	‖f	ADP
ma-154	42	19	′(u)−	′(u)−	PROPN
ma-154	42	20	f	f	PROPN
ma-154	42	21	′(v)‖	′(v)‖	PROPN
ma-154	42	22	≤	≤	PROPN
ma-154	42	23	l‖u	l‖u	VERB
ma-154	42	24	−	−	PROPN
ma-154	42	25	v‖	v‖	NOUN
ma-154	42	26	(	(	PUNCT
ma-154	42	27	2.3	2.3	NUM
ma-154	42	28	)	)	PUNCT
ma-154	42	29	for	for	ADP
ma-154	42	30	all	all	DET
ma-154	42	31	u	u	PROPN
ma-154	42	32	∈	∈	PROPN
ma-154	42	33	ω0	ω0	NOUN
ma-154	42	34	,	,	PUNCT
ma-154	42	35	v	v	NOUN
ma-154	42	36	=	=	SYM
ma-154	42	37	u	u	NOUN
ma-154	42	38	−	−	PROPN
ma-154	42	39	f	f	NOUN
ma-154	42	40	′(u)−1f	′(u)−1f	NOUN
ma-154	42	41	(	(	PUNCT
ma-154	42	42	u	u	NOUN
ma-154	42	43	)	)	PUNCT
ma-154	42	44	∈	∈	PROPN
ma-154	42	45	ω0	ω0	NOUN
ma-154	42	46	.	.	PUNCT
ma-154	43	1	https://doi.org/10.28924/ada/ma.3.15	https://doi.org/10.28924/ada/ma.3.15	NOUN
ma-154	43	2	eur	eur	PROPN
ma-154	43	3	.	.	PUNCT
ma-154	44	1	j.	j.	PROPN
ma-154	44	2	math	math	PROPN
ma-154	44	3	.	.	PUNCT
ma-154	45	1	anal	anal	PROPN
ma-154	45	2	.	.	PUNCT
ma-154	46	1	10.28924	10.28924	NUM
ma-154	46	2	/	/	SYM
ma-154	46	3	ada	ada	PROPN
ma-154	46	4	/	/	SYM
ma-154	46	5	ma.3.15	ma.3.15	NOUN
ma-154	46	6	3	3	NUM
ma-154	46	7	definition	definition	NOUN
ma-154	46	8	2.3	2.3	NUM
ma-154	46	9	.	.	PUNCT
ma-154	47	1	operator	operator	NOUN
ma-154	47	2	f	f	PROPN
ma-154	47	3	′	′	PROPN
ma-154	47	4	is	be	AUX
ma-154	47	5	2−restricted	2−restricte	VERB
ma-154	47	6	lipschitz	lipschitz	NOUN
ma-154	47	7	continuous	continuous	ADJ
ma-154	47	8	on	on	ADP
ma-154	47	9	ω0	ω0	NOUN
ma-154	47	10	if	if	SCONJ
ma-154	47	11	there	there	PRON
ma-154	47	12	exists	exist	VERB
ma-154	47	13	l1	l1	PROPN
ma-154	47	14	>	>	X
ma-154	47	15	0	0	NUM
ma-154	47	16	such	such	ADJ
ma-154	47	17	that	that	PRON
ma-154	47	18	for	for	ADP
ma-154	47	19	all	all	DET
ma-154	47	20	u	u	NOUN
ma-154	47	21	,	,	PUNCT
ma-154	47	22	v	v	PROPN
ma-154	47	23	∈	∈	NOUN
ma-154	47	24	ω0	ω0	NOUN
ma-154	47	25	‖f	‖f	PUNCT
ma-154	47	26	′(u)−	′(u)−	PROPN
ma-154	47	27	f	f	PROPN
ma-154	47	28	′(v)‖	′(v)‖	PROPN
ma-154	47	29	≤	≤	ADV
ma-154	48	1	l1‖u	l1‖u	NOUN
ma-154	48	2	−	−	NOUN
ma-154	49	1	v‖.	v‖.	NOUN
ma-154	49	2	(	(	PUNCT
ma-154	49	3	2.4	2.4	NUM
ma-154	49	4	)	)	PUNCT
ma-154	49	5	definition	definition	NOUN
ma-154	49	6	2.4	2.4	NUM
ma-154	49	7	.	.	PUNCT
ma-154	50	1	operator	operator	NOUN
ma-154	50	2	f	f	PROPN
ma-154	50	3	′	′	NOUN
ma-154	50	4	is	be	AUX
ma-154	50	5	lipschitz	lipschitz	NOUN
ma-154	50	6	continuous	continuous	ADJ
ma-154	50	7	on	on	ADP
ma-154	50	8	ω	ω	NUM
ma-154	50	9	if	if	SCONJ
ma-154	50	10	there	there	PRON
ma-154	50	11	exists	exist	VERB
ma-154	50	12	l2	l2	NOUN
ma-154	50	13	>	>	X
ma-154	50	14	0	0	NUM
ma-154	51	1	such	such	ADJ
ma-154	51	2	that	that	PRON
ma-154	51	3	for	for	ADP
ma-154	51	4	all	all	DET
ma-154	51	5	u	u	NOUN
ma-154	51	6	,	,	PUNCT
ma-154	51	7	v	v	PROPN
ma-154	51	8	∈	∈	PROPN
ma-154	51	9	ω	ω	NOUN
ma-154	51	10	‖f	‖f	SCONJ
ma-154	51	11	′(u)−	′(u)−	PROPN
ma-154	51	12	f	f	PROPN
ma-154	52	1	′(v)‖	′(v)‖	PROPN
ma-154	52	2	≤	≤	NUM
ma-154	52	3	l2‖u	l2‖u	VERB
ma-154	52	4	−	−	PROPN
ma-154	52	5	v‖.	v‖.	NOUN
ma-154	52	6	(	(	PUNCT
ma-154	52	7	2.5	2.5	NUM
ma-154	52	8	)	)	PUNCT
ma-154	52	9	definition	definition	NOUN
ma-154	52	10	2.5	2.5	NUM
ma-154	52	11	.	.	PUNCT
ma-154	53	1	assume	assume	VERB
ma-154	53	2	:	:	PUNCT
ma-154	53	3	λαl0	λαl0	X
ma-154	53	4	<	<	X
ma-154	53	5	1	1	NUM
ma-154	53	6	(	(	PUNCT
ma-154	53	7	2.6	2.6	NUM
ma-154	53	8	)	)	PUNCT
ma-154	53	9	and	and	CCONJ
ma-154	53	10	ω1	ω1	PROPN
ma-154	53	11	=	=	SYM
ma-154	53	12	b(x1	b(x1	NOUN
ma-154	53	13	,	,	PUNCT
ma-154	53	14	1	1	NUM
ma-154	53	15	αl0	αl0	NOUN
ma-154	54	1	−	−	NOUN
ma-154	55	1	‖x1	‖x1	NOUN
ma-154	55	2	−	−	PROPN
ma-154	55	3	x0‖	x0‖	PROPN
ma-154	55	4	)	)	PUNCT
ma-154	56	1	⊂	⊂	PROPN
ma-154	56	2	ω	ω	PROPN
ma-154	56	3	(	(	PUNCT
ma-154	56	4	2.7	2.7	NUM
ma-154	56	5	)	)	PUNCT
ma-154	56	6	then	then	ADV
ma-154	56	7	,	,	PUNCT
ma-154	56	8	operator	operator	NOUN
ma-154	56	9	is	be	AUX
ma-154	56	10	3−	3−	NUM
ma-154	56	11	restricted	restricted	ADJ
ma-154	56	12	lipschitz	lipschitz	NOUN
ma-154	56	13	continuous	continuous	ADJ
ma-154	56	14	on	on	ADP
ma-154	56	15	ω1	ω1	PROPN
ma-154	56	16	if	if	SCONJ
ma-154	56	17	there	there	PRON
ma-154	56	18	exists	exist	VERB
ma-154	56	19	a	a	DET
ma-154	56	20	constant	constant	ADJ
ma-154	56	21	k	k	X
ma-154	56	22	>	>	X
ma-154	56	23	0	0	NUM
ma-154	56	24	such	such	ADJ
ma-154	56	25	that	that	PRON
ma-154	56	26	for	for	ADP
ma-154	56	27	all	all	DET
ma-154	56	28	u	u	PRON
ma-154	56	29	∈	∈	PROPN
ma-154	56	30	ω1	ω1	PROPN
ma-154	56	31	‖f	‖f	SCONJ
ma-154	56	32	′(u)−	′(u)−	PROPN
ma-154	56	33	f	f	PROPN
ma-154	57	1	′(v)‖	′(v)‖	PROPN
ma-154	57	2	≤	≤	NUM
ma-154	57	3	k‖u	k‖u	NOUN
ma-154	57	4	−	−	PROPN
ma-154	57	5	v‖	v‖	NOUN
ma-154	57	6	(	(	PUNCT
ma-154	57	7	2.8	2.8	NUM
ma-154	57	8	)	)	PUNCT
ma-154	57	9	for	for	ADP
ma-154	57	10	v	v	NOUN
ma-154	57	11	=	=	SYM
ma-154	57	12	u	u	NOUN
ma-154	57	13	−	−	PROPN
ma-154	57	14	f	f	NOUN
ma-154	57	15	′(u)−1f	′(u)−1f	NOUN
ma-154	57	16	(	(	PUNCT
ma-154	57	17	u	u	NOUN
ma-154	57	18	)	)	PUNCT
ma-154	57	19	∈	∈	PROPN
ma-154	57	20	ω1	ω1	PROPN
ma-154	57	21	.	.	PROPN
ma-154	57	22	remark	remark	PROPN
ma-154	57	23	2.6	2.6	NUM
ma-154	57	24	.	.	PUNCT
ma-154	58	1	by	by	ADP
ma-154	58	2	the	the	DET
ma-154	58	3	definition	definition	NOUN
ma-154	58	4	of	of	ADP
ma-154	58	5	sets	set	NOUN
ma-154	58	6	ω0	ω0	NOUN
ma-154	58	7	and	and	CCONJ
ma-154	58	8	ω1	ω1	PROPN
ma-154	58	9	,	,	PUNCT
ma-154	58	10	we	we	PRON
ma-154	58	11	get	get	VERB
ma-154	58	12	ω0	ω0	ADV
ma-154	58	13	⊆	⊆	NUM
ma-154	58	14	ω	ω	NUM
ma-154	58	15	,	,	PUNCT
ma-154	58	16	(	(	PUNCT
ma-154	58	17	2.9	2.9	NUM
ma-154	58	18	)	)	PUNCT
ma-154	58	19	and	and	CCONJ
ma-154	58	20	ω1	ω1	PROPN
ma-154	58	21	⊆	⊆	NUM
ma-154	58	22	ω0	ω0	NOUN
ma-154	58	23	.	.	PUNCT
ma-154	59	1	(	(	PUNCT
ma-154	59	2	2.10	2.10	NUM
ma-154	59	3	)	)	PUNCT
ma-154	59	4	indeed	indeed	ADV
ma-154	59	5	,	,	PUNCT
ma-154	59	6	if	if	SCONJ
ma-154	59	7	y	y	PROPN
ma-154	59	8	∈	∈	PROPN
ma-154	59	9	ω1	ω1	PROPN
ma-154	59	10	,	,	PUNCT
ma-154	59	11	then	then	ADV
ma-154	59	12	we	we	PRON
ma-154	59	13	obtain	obtain	VERB
ma-154	59	14	‖y	‖y	PUNCT
ma-154	60	1	−	−	PROPN
ma-154	60	2	x1‖	x1‖	PROPN
ma-154	60	3	≤	≤	NUM
ma-154	60	4	1	1	NUM
ma-154	60	5	αl0	αl0	NOUN
ma-154	60	6	−	−	PROPN
ma-154	60	7	‖x1	‖x1	NOUN
ma-154	60	8	−	−	PROPN
ma-154	60	9	x0‖	x0‖	PROPN
ma-154	60	10	⇒	⇒	PROPN
ma-154	60	11	‖y	‖y	PUNCT
ma-154	61	1	−	−	PROPN
ma-154	61	2	x1‖+	x1‖+	PUNCT
ma-154	62	1	‖x1	‖x1	NOUN
ma-154	62	2	−	−	PROPN
ma-154	62	3	x0‖	x0‖	PROPN
ma-154	62	4	≤	≤	NUM
ma-154	62	5	1	1	NUM
ma-154	62	6	αl0	αl0	NOUN
ma-154	62	7	⇒	⇒	VERB
ma-154	62	8	‖y	‖y	PUNCT
ma-154	63	1	−	−	PROPN
ma-154	64	1	x0‖	x0‖	PROPN
ma-154	64	2	≤	≤	NUM
ma-154	64	3	1	1	NUM
ma-154	64	4	αl0	αl0	NOUN
ma-154	64	5	⇒	⇒	VERB
ma-154	64	6	y	y	PROPN
ma-154	64	7	∈	∈	PROPN
ma-154	64	8	ω0	ω0	PROPN
ma-154	64	9	⇒	⇒	NOUN
ma-154	64	10	ω1	ω1	PROPN
ma-154	64	11	⊆	⊆	NUM
ma-154	64	12	ω0	ω0	NOUN
ma-154	64	13	.	.	PUNCT
ma-154	65	1	it	it	PRON
ma-154	65	2	follows	follow	VERB
ma-154	65	3	by	by	ADP
ma-154	65	4	these	these	DET
ma-154	65	5	definitions	definition	NOUN
ma-154	65	6	,	,	PUNCT
ma-154	65	7	(	(	PUNCT
ma-154	65	8	2.9	2.9	NUM
ma-154	65	9	)	)	PUNCT
ma-154	65	10	and	and	CCONJ
ma-154	65	11	(	(	PUNCT
ma-154	65	12	2.10	2.10	NUM
ma-154	65	13	)	)	PUNCT
ma-154	65	14	that	that	SCONJ
ma-154	65	15	if	if	SCONJ
ma-154	65	16	the	the	DET
ma-154	65	17	best	good	ADJ
ma-154	65	18	constants	constant	NOUN
ma-154	65	19	are	be	AUX
ma-154	65	20	chosen	choose	VERB
ma-154	65	21	in	in	ADP
ma-154	65	22	the	the	DET
ma-154	65	23	definitions	definition	NOUN
ma-154	65	24	2.1	2.1	NUM
ma-154	65	25	-	-	SYM
ma-154	65	26	2.5	2.5	NUM
ma-154	65	27	,	,	PUNCT
ma-154	65	28	then	then	ADV
ma-154	65	29	l	l	PROPN
ma-154	65	30	≤	≤	PROPN
ma-154	65	31	l1	l1	PROPN
ma-154	65	32	≤	≤	PROPN
ma-154	65	33	l2	l2	NOUN
ma-154	65	34	,	,	PUNCT
ma-154	65	35	(	(	PUNCT
ma-154	65	36	2.11	2.11	NUM
ma-154	65	37	)	)	PUNCT
ma-154	65	38	l0	l0	NOUN
ma-154	65	39	≤	≤	NOUN
ma-154	65	40	l2	l2	NOUN
ma-154	65	41	,	,	PUNCT
ma-154	65	42	(	(	PUNCT
ma-154	65	43	2.12	2.12	NUM
ma-154	65	44	)	)	PUNCT
ma-154	65	45	and	and	CCONJ
ma-154	65	46	k	k	PROPN
ma-154	65	47	≤	≤	PROPN
ma-154	65	48	l.	l.	NOUN
ma-154	65	49	(	(	PUNCT
ma-154	65	50	2.13	2.13	NUM
ma-154	65	51	)	)	PUNCT
ma-154	65	52	hence	hence	ADV
ma-154	65	53	,	,	PUNCT
ma-154	65	54	parameter	parameter	PROPN
ma-154	65	55	k	k	PROPN
ma-154	65	56	can	can	AUX
ma-154	65	57	replace	replace	VERB
ma-154	65	58	results	result	NOUN
ma-154	65	59	on	on	ADP
ma-154	65	60	newton	newton	PROPN
ma-154	65	61	’s	’	VERB
ma-154	65	62	using	use	VERB
ma-154	65	63	the	the	DET
ma-154	65	64	constants	constant	NOUN
ma-154	65	65	l	l	NOUN
ma-154	65	66	,	,	PUNCT
ma-154	65	67	l1	l1	PROPN
ma-154	65	68	and	and	CCONJ
ma-154	65	69	l2	l2	NOUN
ma-154	65	70	.	.	PUNCT
ma-154	66	1	notice	notice	NOUN
ma-154	66	2	also	also	ADV
ma-154	66	3	that	that	SCONJ
ma-154	66	4	l0	l0	PROPN
ma-154	66	5	=	=	SYM
ma-154	66	6	l0(f	l0(f	PROPN
ma-154	66	7	′,ω	′,ω	NUM
ma-154	66	8	)	)	PUNCT
ma-154	66	9	,	,	PUNCT
ma-154	66	10	l	l	X
ma-154	67	1	=	=	PUNCT
ma-154	67	2	l(f	l(f	PROPN
ma-154	67	3	′,ω0	′,ω0	NOUN
ma-154	67	4	)	)	PUNCT
ma-154	67	5	,	,	PUNCT
ma-154	67	6	l1	l1	PROPN
ma-154	67	7	=	=	PROPN
ma-154	68	1	l1(f	l1(f	X
ma-154	68	2	′,ω0	′,ω0	NOUN
ma-154	68	3	)	)	PUNCT
ma-154	68	4	,	,	PUNCT
ma-154	68	5	l2	l2	NOUN
ma-154	68	6	=	=	SYM
ma-154	68	7	l2(f	l2(f	X
ma-154	68	8	′,ω	′,ω	X
ma-154	68	9	)	)	PUNCT
ma-154	68	10	and	and	CCONJ
ma-154	68	11	k	k	PROPN
ma-154	68	12	=	=	SYM
ma-154	68	13	k(f	k(f	PROPN
ma-154	68	14	,	,	PUNCT
ma-154	68	15	ω0,ω1	ω0,ω1	PROPN
ma-154	68	16	)	)	PUNCT
ma-154	68	17	.	.	PUNCT
ma-154	69	1	examples	example	NOUN
ma-154	69	2	,	,	PUNCT
ma-154	69	3	where	where	SCONJ
ma-154	69	4	(	(	PUNCT
ma-154	69	5	2.9)-(2.13	2.9)-(2.13	NUM
ma-154	69	6	)	)	PUNCT
ma-154	69	7	are	be	AUX
ma-154	69	8	strict	strict	ADJ
ma-154	69	9	can	can	AUX
ma-154	69	10	be	be	AUX
ma-154	69	11	found	find	VERB
ma-154	69	12	in	in	ADP
ma-154	69	13	the	the	DET
ma-154	69	14	numerical	numerical	ADJ
ma-154	69	15	section	section	NOUN
ma-154	69	16	.	.	PUNCT
ma-154	70	1	https://doi.org/10.28924/ada/ma.3.15	https://doi.org/10.28924/ada/ma.3.15	NOUN
ma-154	70	2	eur	eur	PROPN
ma-154	70	3	.	.	PUNCT
ma-154	71	1	j.	j.	PROPN
ma-154	71	2	math	math	PROPN
ma-154	71	3	.	.	PUNCT
ma-154	72	1	anal	anal	PROPN
ma-154	72	2	.	.	PUNCT
ma-154	73	1	10.28924	10.28924	NUM
ma-154	73	2	/	/	SYM
ma-154	73	3	ada	ada	PROPN
ma-154	73	4	/	/	SYM
ma-154	73	5	ma.3.15	ma.3.15	NOUN
ma-154	73	6	4	4	NUM
ma-154	73	7	notice	notice	NOUN
ma-154	73	8	that	that	SCONJ
ma-154	73	9	the	the	DET
ma-154	73	10	computation	computation	NOUN
ma-154	73	11	of	of	ADP
ma-154	73	12	the	the	DET
ma-154	73	13	constant	constant	ADJ
ma-154	73	14	l2	l2	NOUN
ma-154	73	15	requires	require	VERB
ma-154	73	16	the	the	DET
ma-154	73	17	computation	computation	NOUN
ma-154	73	18	of	of	ADP
ma-154	73	19	the	the	DET
ma-154	73	20	other	other	ADJ
ma-154	73	21	constants	constant	NOUN
ma-154	73	22	as	as	ADP
ma-154	73	23	special	special	ADJ
ma-154	73	24	cases	case	NOUN
ma-154	73	25	.	.	PUNCT
ma-154	74	1	hence	hence	ADV
ma-154	74	2	,	,	PUNCT
ma-154	74	3	no	no	DET
ma-154	74	4	additional	additional	ADJ
ma-154	74	5	effort	effort	NOUN
ma-154	74	6	is	be	AUX
ma-154	74	7	needed	need	VERB
ma-154	74	8	to	to	PART
ma-154	74	9	compute	compute	VERB
ma-154	74	10	them	they	PRON
ma-154	74	11	.	.	PUNCT
ma-154	75	1	moreover	moreover	ADV
ma-154	75	2	,	,	PUNCT
ma-154	75	3	they	they	PRON
ma-154	75	4	all	all	PRON
ma-154	75	5	depend	depend	VERB
ma-154	75	6	on	on	ADP
ma-154	75	7	the	the	DET
ma-154	75	8	initial	initial	ADJ
ma-154	75	9	data	datum	NOUN
ma-154	75	10	(	(	PUNCT
ma-154	75	11	x0	x0	PROPN
ma-154	75	12	,	,	PUNCT
ma-154	75	13	f	f	PROPN
ma-154	75	14	,	,	PUNCT
ma-154	75	15	ω	ω	PROPN
ma-154	75	16	)	)	PUNCT
ma-154	75	17	.	.	PUNCT
ma-154	76	1	it	it	PRON
ma-154	76	2	is	be	AUX
ma-154	76	3	also	also	ADV
ma-154	76	4	worth	worth	ADJ
ma-154	76	5	noticing	notice	VERB
ma-154	76	6	that	that	SCONJ
ma-154	76	7	under	under	ADP
ma-154	76	8	(	(	PUNCT
ma-154	76	9	2.1	2.1	NUM
ma-154	76	10	)	)	PUNCT
ma-154	76	11	we	we	PRON
ma-154	76	12	obtain	obtain	VERB
ma-154	76	13	‖f	‖f	PRON
ma-154	76	14	′(u)−1‖	′(u)−1‖	NOUN
ma-154	76	15	≤	≤	NUM
ma-154	77	1	α	α	PRON
ma-154	77	2	1−	1−	NUM
ma-154	77	3	αl0‖u	αl0‖u	NOUN
ma-154	77	4	−	−	PROPN
ma-154	77	5	x0‖	x0‖	PROPN
ma-154	77	6	.	.	PUNCT
ma-154	78	1	(	(	PUNCT
ma-154	78	2	2.14	2.14	NUM
ma-154	78	3	)	)	PUNCT
ma-154	78	4	this	this	PRON
ma-154	78	5	is	be	AUX
ma-154	78	6	a	a	DET
ma-154	78	7	tighter	tight	ADJ
ma-154	78	8	estimate	estimate	NOUN
ma-154	78	9	than	than	ADP
ma-154	78	10	using	use	VERB
ma-154	78	11	the	the	DET
ma-154	78	12	stronger	strong	ADJ
ma-154	78	13	(	(	PUNCT
ma-154	78	14	2.5	2.5	NUM
ma-154	78	15	)	)	PUNCT
ma-154	78	16	to	to	PART
ma-154	78	17	get	get	VERB
ma-154	78	18	‖f	‖f	PRON
ma-154	78	19	′(u)−1‖	′(u)−1‖	NOUN
ma-154	78	20	≤	≤	NUM
ma-154	79	1	α	α	DET
ma-154	79	2	1−	1−	NUM
ma-154	79	3	αl2‖u	αl2‖u	NUM
ma-154	79	4	−	−	PROPN
ma-154	80	1	x0‖	x0‖	PROPN
ma-154	80	2	.	.	PUNCT
ma-154	81	1	(	(	PUNCT
ma-154	81	2	2.15	2.15	NUM
ma-154	81	3	)	)	PUNCT
ma-154	81	4	we	we	PRON
ma-154	81	5	assume	assume	VERB
ma-154	81	6	from	from	ADP
ma-154	81	7	now	now	ADV
ma-154	81	8	on	on	ADV
ma-154	81	9	that	that	DET
ma-154	81	10	l0	l0	PROPN
ma-154	81	11	≤	≤	PROPN
ma-154	81	12	k.	k.	PROPN
ma-154	82	1	(	(	PUNCT
ma-154	82	2	2.16	2.16	NUM
ma-154	82	3	)	)	PUNCT
ma-154	83	1	but	but	CCONJ
ma-154	83	2	if	if	SCONJ
ma-154	83	3	k	k	PROPN
ma-154	83	4	<	<	X
ma-154	83	5	l0	l0	PROPN
ma-154	83	6	then	then	ADV
ma-154	83	7	,	,	PUNCT
ma-154	83	8	the	the	DET
ma-154	83	9	following	follow	VERB
ma-154	83	10	results	result	NOUN
ma-154	83	11	hold	hold	VERB
ma-154	83	12	with	with	ADP
ma-154	83	13	l0	l0	NOUN
ma-154	83	14	replacing	replace	VERB
ma-154	83	15	k.	k.	PROPN
ma-154	83	16	based	base	VERB
ma-154	83	17	on	on	ADP
ma-154	83	18	the	the	DET
ma-154	83	19	above	above	ADV
ma-154	83	20	we	we	PRON
ma-154	83	21	present	present	VERB
ma-154	83	22	two	two	NUM
ma-154	83	23	extended	extended	ADJ
ma-154	83	24	theorems	theorem	NOUN
ma-154	83	25	on	on	ADP
ma-154	83	26	newton	newton	PROPN
ma-154	83	27	’s	’s	PART
ma-154	83	28	method	method	NOUN
ma-154	83	29	.	.	PUNCT
ma-154	84	1	an	an	DET
ma-154	84	2	important	important	ADJ
ma-154	84	3	role	role	NOUN
ma-154	84	4	is	be	AUX
ma-154	84	5	played	play	VERB
ma-154	84	6	in	in	ADP
ma-154	84	7	the	the	DET
ma-154	84	8	convergence	convergence	NOUN
ma-154	84	9	of	of	ADP
ma-154	84	10	nm	nm	NOUN
ma-154	84	11	by	by	ADP
ma-154	84	12	the	the	DET
ma-154	84	13	majorizing	majorize	VERB
ma-154	84	14	sequence	sequence	NOUN
ma-154	84	15	{	{	PUNCT
ma-154	84	16	sn	sn	NOUN
ma-154	84	17	}	}	PUNCT
ma-154	84	18	definedby	definedby	ADJ
ma-154	84	19	s0	s0	NOUN
ma-154	84	20	=	=	SYM
ma-154	84	21	0	0	NUM
ma-154	84	22	,	,	PUNCT
ma-154	84	23	sn+1	sn+1	VERB
ma-154	84	24	−	−	PROPN
ma-154	84	25	sn	sn	NOUN
ma-154	84	26	=	=	SYM
ma-154	84	27	−	−	PROPN
ma-154	84	28	p(sn	p(sn	PROPN
ma-154	84	29	)	)	PUNCT
ma-154	84	30	p′0(sn	p′0(sn	PUNCT
ma-154	84	31	)	)	PUNCT
ma-154	84	32	=	=	SYM
ma-154	84	33	αk(sn	αk(sn	ADV
ma-154	84	34	−	−	ADP
ma-154	84	35	sn−1)2	sn−1)2	ADJ
ma-154	84	36	1−	1−	NUM
ma-154	84	37	l0αsn	l0αsn	NOUN
ma-154	84	38	,	,	PUNCT
ma-154	84	39	p(s	p(s	NUM
ma-154	84	40	)	)	PUNCT
ma-154	85	1	=	=	SYM
ma-154	85	2	k	k	PROPN
ma-154	85	3	2	2	NUM
ma-154	85	4	s2	s2	NOUN
ma-154	85	5	−	−	PROPN
ma-154	85	6	s	s	NOUN
ma-154	85	7	α	α	NOUN
ma-154	85	8	+	+	X
ma-154	85	9	λ	λ	PROPN
ma-154	85	10	α	α	NOUN
ma-154	85	11	,	,	PUNCT
ma-154	85	12	p0(s	p0(s	X
ma-154	85	13	)	)	PUNCT
ma-154	85	14	=	=	SYM
ma-154	85	15	l0	l0	PROPN
ma-154	85	16	2	2	NUM
ma-154	85	17	s2	s2	NOUN
ma-154	85	18	−	−	PROPN
ma-154	85	19	s	s	PROPN
ma-154	85	20	α	α	PROPN
ma-154	85	21	λ	λ	PROPN
ma-154	85	22	α	α	X
ma-154	85	23	.	.	PUNCT
ma-154	86	1	theorem	theorem	ADJ
ma-154	86	2	2.7	2.7	NUM
ma-154	86	3	.	.	PUNCT
ma-154	87	1	(	(	PUNCT
ma-154	87	2	extended	extend	VERB
ma-154	87	3	newton	newton	PROPN
ma-154	87	4	-	-	PUNCT
ma-154	87	5	kantorovich	kantorovich	PROPN
ma-154	87	6	theorem	theorem	NOUN
ma-154	87	7	[	[	X
ma-154	87	8	1,2,10,12,13,15,16	1,2,10,12,13,15,16	NUM
ma-154	87	9	]	]	PUNCT
ma-154	87	10	)	)	PUNCT
ma-154	87	11	under	under	ADP
ma-154	87	12	conditions	condition	NOUN
ma-154	87	13	(	(	PUNCT
ma-154	87	14	2.1	2.1	NUM
ma-154	87	15	)	)	PUNCT
ma-154	87	16	,	,	PUNCT
ma-154	87	17	(	(	PUNCT
ma-154	87	18	2.6)-(2.8	2.6)-(2.8	ADJ
ma-154	87	19	)	)	PUNCT
ma-154	87	20	further	far	ADV
ma-154	87	21	suppose	suppose	VERB
ma-154	87	22	b(x0	b(x0	NOUN
ma-154	87	23	,	,	PUNCT
ma-154	87	24	s∗	s∗	PROPN
ma-154	87	25	)	)	PUNCT
ma-154	88	1	⊂	⊂	PROPN
ma-154	88	2	ω	ω	PROPN
ma-154	88	3	,	,	PUNCT
ma-154	88	4	h	h	PROPN
ma-154	88	5	=	=	PRON
ma-154	88	6	kαλ	kαλ	VERB
ma-154	88	7	≤	≤	NUM
ma-154	88	8	1	1	NUM
ma-154	88	9	2	2	NUM
ma-154	88	10	.	.	PUNCT
ma-154	89	1	(	(	PUNCT
ma-154	89	2	2.17	2.17	NUM
ma-154	89	3	)	)	PUNCT
ma-154	89	4	then	then	ADV
ma-154	89	5	,	,	PUNCT
ma-154	89	6	newton	newton	PROPN
ma-154	89	7	’s	’s	PART
ma-154	89	8	method	method	NOUN
ma-154	89	9	(	(	PUNCT
ma-154	89	10	1.2	1.2	NUM
ma-154	89	11	)	)	PUNCT
ma-154	89	12	initiated	initiate	VERB
ma-154	89	13	at	at	ADP
ma-154	89	14	x0	x0	PROPN
ma-154	89	15	∈	∈	PROPN
ma-154	89	16	ω	ω	PROPN
ma-154	89	17	generates	generate	VERB
ma-154	89	18	a	a	DET
ma-154	89	19	sequence	sequence	NOUN
ma-154	89	20	{	{	PUNCT
ma-154	89	21	xn	xn	NOUN
ma-154	89	22	}	}	PUNCT
ma-154	89	23	such	such	ADJ
ma-154	89	24	that:{xn	that:{xn	NOUN
ma-154	89	25	}	}	PUNCT
ma-154	89	26	⊆	⊆	NUM
ma-154	89	27	b(x0	b(x0	NOUN
ma-154	89	28	,	,	PUNCT
ma-154	89	29	s∗	s∗	PROPN
ma-154	89	30	)	)	PUNCT
ma-154	89	31	,	,	PUNCT
ma-154	89	32	limn−→∞	limn−→∞	NOUN
ma-154	89	33	xn	xn	PROPN
ma-154	90	1	=	=	PUNCT
ma-154	90	2	x∗	x∗	PROPN
ma-154	90	3	∈	∈	PROPN
ma-154	90	4	b[x0	b[x0	PROPN
ma-154	90	5	,	,	PUNCT
ma-154	90	6	s∗	s∗	PROPN
ma-154	90	7	]	]	PUNCT
ma-154	90	8	.	.	PUNCT
ma-154	90	9	‖xn+1	‖xn+1	NUM
ma-154	91	1	−	−	NOUN
ma-154	91	2	xn‖	xn‖	PROPN
ma-154	91	3	≤	≤	PROPN
ma-154	91	4	sn+1	sn+1	VERB
ma-154	91	5	−	−	PROPN
ma-154	91	6	sn	sn	PROPN
ma-154	91	7	(	(	PUNCT
ma-154	91	8	2.18	2.18	NUM
ma-154	91	9	)	)	PUNCT
ma-154	91	10	‖x∗	‖x∗	PUNCT
ma-154	91	11	−	−	PROPN
ma-154	92	1	xn‖	xn‖	PROPN
ma-154	92	2	≤	≤	PROPN
ma-154	92	3	s∗	s∗	VERB
ma-154	92	4	−	−	PROPN
ma-154	92	5	sn	sn	PROPN
ma-154	92	6	,	,	PUNCT
ma-154	92	7	(	(	PUNCT
ma-154	92	8	2.19	2.19	NUM
ma-154	92	9	)	)	PUNCT
ma-154	92	10	where	where	SCONJ
ma-154	92	11	,	,	PUNCT
ma-154	92	12	limn−→∞	limn−→∞	PROPN
ma-154	92	13	sn	sn	NOUN
ma-154	92	14	=	=	PUNCT
ma-154	92	15	s∗	s∗	PROPN
ma-154	92	16	=	=	SYM
ma-154	92	17	1−	1−	NUM
ma-154	92	18	√	√	NUM
ma-154	92	19	1−2h	1−2h	NUM
ma-154	92	20	kα	kα	NOUN
ma-154	92	21	and	and	CCONJ
ma-154	92	22	s∗∗	s∗∗	X
ma-154	92	23	=	=	SYM
ma-154	92	24	1	1	NUM
ma-154	92	25	+	+	NUM
ma-154	92	26	√	√	PROPN
ma-154	92	27	1−2h	1−2h	NUM
ma-154	92	28	kα	kα	NOUN
ma-154	92	29	.	.	PUNCT
ma-154	93	1	moreover	moreover	ADV
ma-154	93	2	,	,	PUNCT
ma-154	93	3	the	the	DET
ma-154	93	4	following	follow	VERB
ma-154	93	5	items	item	NOUN
ma-154	93	6	hold	hold	VERB
ma-154	93	7	for	for	ADP
ma-154	93	8	τ	τ	PROPN
ma-154	93	9	=	=	X
ma-154	93	10	s∗	s∗	PROPN
ma-154	93	11	s∗∗	s∗∗	ADV
ma-154	93	12	s∗	s∗	PROPN
ma-154	93	13	−	−	PROPN
ma-154	93	14	sn	sn	NOUN
ma-154	93	15	=	=	PUNCT
ma-154	93	16	{	{	PUNCT
ma-154	93	17	(	(	PUNCT
ma-154	93	18	s∗∗−s∗)τ2	s∗∗−s∗)τ2	PROPN
ma-154	93	19	n	n	PRON
ma-154	93	20	1−τ2n	1−τ2n	NUM
ma-154	93	21	,	,	PUNCT
ma-154	93	22	if	if	SCONJ
ma-154	93	23	s∗	s∗	PROPN
ma-154	93	24	<	<	X
ma-154	93	25	s∗∗	s∗∗	PROPN
ma-154	93	26	1	1	NUM
ma-154	93	27	2n	2n	NUM
ma-154	93	28	s∗	s∗	PROPN
ma-154	93	29	,	,	PUNCT
ma-154	93	30	if	if	SCONJ
ma-154	93	31	s∗	s∗	PROPN
ma-154	93	32	=	=	PUNCT
ma-154	93	33	s∗∗.	s∗∗.	PROPN
ma-154	93	34	https://doi.org/10.28924/ada/ma.3.15	https://doi.org/10.28924/ada/ma.3.15	NOUN
ma-154	93	35	eur	eur	NOUN
ma-154	93	36	.	.	PUNCT
ma-154	94	1	j.	j.	PROPN
ma-154	94	2	math	math	PROPN
ma-154	94	3	.	.	PUNCT
ma-154	95	1	anal	anal	PROPN
ma-154	95	2	.	.	PUNCT
ma-154	96	1	10.28924	10.28924	NUM
ma-154	96	2	/	/	SYM
ma-154	96	3	ada	ada	PROPN
ma-154	96	4	/	/	SYM
ma-154	96	5	ma.3.15	ma.3.15	NOUN
ma-154	96	6	5	5	NUM
ma-154	96	7	furthermore	furthermore	ADV
ma-154	96	8	,	,	PUNCT
ma-154	96	9	the	the	DET
ma-154	96	10	element	element	NOUN
ma-154	96	11	x∗	x∗	PROPN
ma-154	96	12	is	be	AUX
ma-154	96	13	the	the	DET
ma-154	96	14	unique	unique	ADJ
ma-154	96	15	solution	solution	NOUN
ma-154	96	16	of	of	ADP
ma-154	96	17	equation	equation	NOUN
ma-154	96	18	f	f	X
ma-154	96	19	(	(	PUNCT
ma-154	96	20	x	x	X
ma-154	96	21	)	)	PUNCT
ma-154	96	22	=	=	SYM
ma-154	96	23	0	0	NUM
ma-154	96	24	in	in	ADP
ma-154	96	25	b[x0	b[x0	ADV
ma-154	96	26	,	,	PUNCT
ma-154	96	27	s̄	s̄	NOUN
ma-154	96	28	]	]	PUNCT
ma-154	96	29	,	,	PUNCT
ma-154	96	30	where	where	SCONJ
ma-154	96	31	s̄	s̄	NOUN
ma-154	96	32	=	=	SYM
ma-154	96	33	2	2	NUM
ma-154	96	34	l0α	l0α	PROPN
ma-154	96	35	−	−	PROPN
ma-154	96	36	s∗	s∗	NOUN
ma-154	96	37	if	if	SCONJ
ma-154	96	38	l0αs∗	l0αs∗	PROPN
ma-154	96	39	<	<	X
ma-154	96	40	2	2	X
ma-154	96	41	.	.	PUNCT
ma-154	96	42	proof	proof	NOUN
ma-154	96	43	.	.	PUNCT
ma-154	97	1	simply	simply	ADV
ma-154	97	2	replace	replace	VERB
ma-154	97	3	l2	l2	NOUN
ma-154	97	4	by	by	ADP
ma-154	97	5	k	k	PROPN
ma-154	97	6	and	and	CCONJ
ma-154	97	7	use	use	NOUN
ma-154	97	8	(	(	PUNCT
ma-154	97	9	2.14	2.14	NUM
ma-154	97	10	)	)	PUNCT
ma-154	97	11	instead	instead	ADV
ma-154	97	12	of	of	ADP
ma-154	97	13	(	(	PUNCT
ma-154	97	14	2.15	2.15	NUM
ma-154	97	15	)	)	PUNCT
ma-154	97	16	in	in	ADP
ma-154	97	17	the	the	DET
ma-154	97	18	proof	proof	NOUN
ma-154	97	19	of	of	ADP
ma-154	97	20	the	the	DET
ma-154	97	21	version	version	NOUN
ma-154	97	22	ofnewton	ofnewton	PROPN
ma-154	97	23	-	-	PUNCT
ma-154	97	24	kantorovich	kantorovich	NOUN
ma-154	97	25	theorem	theorem	NOUN
ma-154	97	26	given	give	VERB
ma-154	97	27	in	in	ADP
ma-154	97	28	[	[	X
ma-154	97	29	10	10	NUM
ma-154	97	30	]	]	PUNCT
ma-154	97	31	(	(	PUNCT
ma-154	97	32	see	see	VERB
ma-154	97	33	also	also	ADV
ma-154	97	34	[	[	X
ma-154	97	35	3–9,14–16	3–9,14–16	NUM
ma-154	97	36	]	]	X
ma-154	97	37	.	.	PUNCT
ma-154	98	1	�	�	PROPN
ma-154	98	2	remark	remark	VERB
ma-154	98	3	2.8	2.8	NUM
ma-154	98	4	.	.	PUNCT
ma-154	99	1	(	(	PUNCT
ma-154	99	2	i)if	i)if	NOUN
ma-154	99	3	k	k	NOUN
ma-154	99	4	=	=	SYM
ma-154	99	5	l2	l2	PROPN
ma-154	99	6	,	,	PUNCT
ma-154	99	7	the	the	DET
ma-154	99	8	result	result	NOUN
ma-154	99	9	of	of	ADP
ma-154	99	10	theorem	theorem	ADJ
ma-154	99	11	2.7	2.7	NUM
ma-154	99	12	reduces	reduce	VERB
ma-154	99	13	to	to	ADP
ma-154	99	14	one	one	NUM
ma-154	99	15	in	in	ADP
ma-154	99	16	the	the	DET
ma-154	99	17	newton	newton	PROPN
ma-154	99	18	-	-	PUNCT
ma-154	99	19	kantorovich	kantorovich	PROPN
ma-154	99	20	theorem	theorem	NOUN
ma-154	99	21	where	where	SCONJ
ma-154	99	22	hk	hk	PROPN
ma-154	99	23	=	=	PUNCT
ma-154	99	24	l2αλ	l2αλ	PUNCT
ma-154	99	25	≤	≤	NUM
ma-154	99	26	1	1	NUM
ma-154	99	27	2	2	NUM
ma-154	99	28	,	,	PUNCT
ma-154	99	29	(	(	PUNCT
ma-154	99	30	2.20	2.20	NUM
ma-154	99	31	)	)	PUNCT
ma-154	99	32	t0	t0	NOUN
ma-154	99	33	=	=	SYM
ma-154	99	34	0	0	NUM
ma-154	99	35	,	,	PUNCT
ma-154	99	36	tn+1	tn+1	NOUN
ma-154	99	37	−	−	PROPN
ma-154	99	38	tn	tn	NOUN
ma-154	99	39	=	=	SYM
ma-154	99	40	−	−	NOUN
ma-154	99	41	p̄(tn	p̄(tn	ADJ
ma-154	99	42	)	)	PUNCT
ma-154	99	43	p̄′(tn	p̄′(tn	NOUN
ma-154	99	44	)	)	PUNCT
ma-154	99	45	=	=	SYM
ma-154	99	46	αl2(tn	αl2(tn	NUM
ma-154	100	1	−	−	NOUN
ma-154	100	2	tn−1)2	tn−1)2	VERB
ma-154	100	3	1−	1−	NUM
ma-154	100	4	l2αtn	l2αtn	NOUN
ma-154	100	5	,	,	PUNCT
ma-154	100	6	p̄(s	p̄(s	NOUN
ma-154	100	7	)	)	PUNCT
ma-154	100	8	=	=	SYM
ma-154	100	9	l2	l2	NOUN
ma-154	100	10	2	2	NUM
ma-154	100	11	s2	s2	NOUN
ma-154	100	12	−	−	PROPN
ma-154	100	13	s	s	NOUN
ma-154	100	14	α	α	NOUN
ma-154	101	1	+	+	NOUN
ma-154	102	1	λ	λ	X
ma-154	102	2	α	α	NOUN
ma-154	102	3	,	,	PUNCT
ma-154	102	4	and	and	CCONJ
ma-154	102	5	limn−→∞	limn−→∞	PROPN
ma-154	102	6	tn	tn	NOUN
ma-154	102	7	=	=	SYM
ma-154	102	8	t∗	t∗	PROPN
ma-154	102	9	=	=	SYM
ma-154	102	10	1−	1−	NUM
ma-154	102	11	√	√	PROPN
ma-154	102	12	1−2kk	1−2kk	NUM
ma-154	102	13	l2α	l2α	PROPN
ma-154	102	14	and	and	CCONJ
ma-154	103	1	t∗∗	t∗∗	ADP
ma-154	103	2	=	=	NOUN
ma-154	103	3	1	1	NUM
ma-154	103	4	+	+	NUM
ma-154	103	5	√	√	PROPN
ma-154	103	6	1−2kk	1−2kk	NUM
ma-154	103	7	l2α	l2α	PROPN
ma-154	103	8	,	,	PUNCT
ma-154	103	9	¯̄s	¯̄s	PROPN
ma-154	103	10	=	=	SYM
ma-154	103	11	2	2	NUM
ma-154	103	12	l2α	l2α	PROPN
ma-154	103	13	−	−	PROPN
ma-154	103	14	t∗	t∗	PROPN
ma-154	103	15	,	,	PUNCT
ma-154	103	16	µ	µ	NOUN
ma-154	103	17	=	=	SYM
ma-154	103	18	t∗	t∗	NOUN
ma-154	103	19	t∗∗	t∗∗	ADJ
ma-154	103	20	,	,	PUNCT
ma-154	103	21	t∗	t∗	NOUN
ma-154	103	22	−	−	NOUN
ma-154	103	23	tn	tn	NOUN
ma-154	103	24	=	=	PUNCT
ma-154	103	25			PUNCT
ma-154	103	26	(	(	PUNCT
ma-154	103	27	t∗∗−t∗)µ2	t∗∗−t∗)µ2	PROPN
ma-154	103	28	n	n	NUM
ma-154	103	29	1−µ2n	1−µ2n	NUM
ma-154	103	30	,	,	PUNCT
ma-154	103	31	if	if	SCONJ
ma-154	103	32	t∗	t∗	NOUN
ma-154	103	33	<	<	X
ma-154	103	34	t∗∗	t∗∗	ADP
ma-154	103	35	1	1	NUM
ma-154	103	36	2n	2n	NUM
ma-154	103	37	t∗	t∗	NOUN
ma-154	103	38	,	,	PUNCT
ma-154	103	39	if	if	SCONJ
ma-154	103	40	t∗	t∗	NOUN
ma-154	103	41	=	=	SYM
ma-154	103	42	t∗∗.	t∗∗.	NOUN
ma-154	103	43	then	then	ADV
ma-154	103	44	,	,	PUNCT
ma-154	103	45	in	in	ADP
ma-154	103	46	view	view	NOUN
ma-154	103	47	of	of	ADP
ma-154	103	48	estimates	estimate	NOUN
ma-154	103	49	(	(	PUNCT
ma-154	103	50	2.11)-(2.13	2.11)-(2.13	NUM
ma-154	103	51	)	)	PUNCT
ma-154	103	52	we	we	PRON
ma-154	103	53	have	have	VERB
ma-154	103	54	hk	hk	PROPN
ma-154	103	55	≤	≤	ADJ
ma-154	103	56	1	1	NUM
ma-154	103	57	2	2	NUM
ma-154	103	58	⇒	⇒	NOUN
ma-154	103	59	h	h	NOUN
ma-154	104	1	≤	≤	ADV
ma-154	104	2	1	1	NUM
ma-154	104	3	2	2	NUM
ma-154	104	4	,	,	PUNCT
ma-154	104	5	(	(	PUNCT
ma-154	104	6	2.21	2.21	NUM
ma-154	104	7	)	)	PUNCT
ma-154	104	8	s∗	s∗	PROPN
ma-154	104	9	≤	≤	ADJ
ma-154	104	10	t∗	t∗	NOUN
ma-154	104	11	,	,	PUNCT
ma-154	104	12	¯̄s	¯̄s	ADJ
ma-154	104	13	≤	≤	NUM
ma-154	104	14	s̄	s̄	NOUN
ma-154	104	15	,	,	PUNCT
ma-154	104	16	(	(	PUNCT
ma-154	104	17	2.22	2.22	NUM
ma-154	104	18	)	)	PUNCT
ma-154	104	19	0	0	NUM
ma-154	105	1	≤	≤	NOUN
ma-154	105	2	sn+1	sn+1	VERB
ma-154	105	3	−	−	PROPN
ma-154	105	4	sn	sn	PROPN
ma-154	105	5	≤	≤	PROPN
ma-154	105	6	tn+1	tn+1	PROPN
ma-154	105	7	−	−	PROPN
ma-154	105	8	tn	tn	PROPN
ma-154	105	9	(	(	PUNCT
ma-154	105	10	2.23	2.23	NUM
ma-154	105	11	)	)	PUNCT
ma-154	105	12	and	and	CCONJ
ma-154	105	13	0	0	NUM
ma-154	105	14	≤	≤	NOUN
ma-154	105	15	s∗	s∗	PROPN
ma-154	105	16	−	−	PROPN
ma-154	105	17	sn	sn	PROPN
ma-154	105	18	≤	≤	PROPN
ma-154	105	19	t∗	t∗	NOUN
ma-154	105	20	−	−	PROPN
ma-154	105	21	tn	tn	PROPN
ma-154	105	22	.	.	PUNCT
ma-154	106	1	(	(	PUNCT
ma-154	106	2	2.24	2.24	NUM
ma-154	106	3	)	)	PUNCT
ma-154	106	4	estimates	estimate	NOUN
ma-154	106	5	(	(	PUNCT
ma-154	106	6	2.21)-(2.24	2.21)-(2.24	NUM
ma-154	106	7	)	)	PUNCT
ma-154	106	8	justify	justify	VERB
ma-154	106	9	the	the	DET
ma-154	106	10	advantages	advantage	NOUN
ma-154	106	11	(	(	PUNCT
ma-154	106	12	a	a	X
ma-154	106	13	)	)	PUNCT
ma-154	106	14	as	as	SCONJ
ma-154	106	15	stated	state	VERB
ma-154	106	16	in	in	ADP
ma-154	106	17	the	the	DET
ma-154	106	18	introduction	introduction	NOUN
ma-154	106	19	.	.	PUNCT
ma-154	107	1	(	(	PUNCT
ma-154	107	2	ii)a	ii)a	NOUN
ma-154	107	3	more	more	ADV
ma-154	107	4	careful	careful	ADJ
ma-154	107	5	look	look	NOUN
ma-154	107	6	at	at	ADP
ma-154	107	7	the	the	DET
ma-154	107	8	proof	proof	NOUN
ma-154	107	9	shows	show	VERB
ma-154	107	10	that	that	SCONJ
ma-154	107	11	tighter	tight	ADJ
ma-154	107	12	sequence	sequence	NOUN
ma-154	107	13	{	{	PUNCT
ma-154	107	14	rn	rn	NOUN
ma-154	107	15	}	}	PUNCT
ma-154	107	16	defined	define	VERB
ma-154	107	17	by	by	ADP
ma-154	107	18	r0	r0	NOUN
ma-154	107	19	=	=	SYM
ma-154	107	20	0	0	NUM
ma-154	107	21	,	,	PUNCT
ma-154	107	22	r1	r1	NOUN
ma-154	107	23	=	=	SYM
ma-154	107	24	λ	λ	PROPN
ma-154	107	25	,	,	PUNCT
ma-154	107	26	r2	r2	PROPN
ma-154	107	27	=	=	PROPN
ma-154	107	28	r1	r1	PROPN
ma-154	107	29	+	+	CCONJ
ma-154	107	30	αl0(r1	αl0(r1	NOUN
ma-154	107	31	−	−	PROPN
ma-154	107	32	r0)2	r0)2	ADP
ma-154	107	33	2(1−	2(1−	NUM
ma-154	107	34	l0αr1	l0αr1	NOUN
ma-154	107	35	)	)	PUNCT
ma-154	107	36	,	,	PUNCT
ma-154	107	37	rn+2	rn+2	X
ma-154	107	38	=	=	PUNCT
ma-154	107	39	rn+1	rn+1	PROPN
ma-154	107	40	+	+	X
ma-154	107	41	kα(rn+1	kα(rn+1	VERB
ma-154	107	42	−	−	PROPN
ma-154	107	43	rn)2	rn)2	PROPN
ma-154	107	44	2(1−	2(1−	PROPN
ma-154	107	45	l0αrn+1	l0αrn+1	NOUN
ma-154	107	46	)	)	PUNCT
ma-154	107	47	,	,	PUNCT
ma-154	107	48	also	also	ADV
ma-154	107	49	majorizes	majorize	VERB
ma-154	107	50	sequence	sequence	NOUN
ma-154	107	51	{	{	PUNCT
ma-154	107	52	xn	xn	NUM
ma-154	107	53	}	}	PUNCT
ma-154	107	54	.	.	PUNCT
ma-154	108	1	the	the	DET
ma-154	108	2	sufficient	sufficient	ADJ
ma-154	108	3	convergence	convergence	NOUN
ma-154	108	4	criterion	criterion	NOUN
ma-154	108	5	for	for	ADP
ma-154	108	6	this	this	DET
ma-154	108	7	sequence	sequence	NOUN
ma-154	108	8	is	be	AUX
ma-154	108	9	given	give	VERB
ma-154	108	10	by	by	ADP
ma-154	108	11	ha	ha	INTJ
ma-154	108	12	=	=	PROPN
ma-154	108	13	k̄αλ	k̄αλ	PROPN
ma-154	108	14	≤	≤	NUM
ma-154	108	15	1	1	NUM
ma-154	108	16	2	2	NUM
ma-154	108	17	,	,	PUNCT
ma-154	108	18	(	(	PUNCT
ma-154	108	19	2.25	2.25	NUM
ma-154	108	20	)	)	PUNCT
ma-154	108	21	https://doi.org/10.28924/ada/ma.3.15	https://doi.org/10.28924/ada/ma.3.15	NOUN
ma-154	108	22	eur	eur	NOUN
ma-154	108	23	.	.	PUNCT
ma-154	109	1	j.	j.	PROPN
ma-154	109	2	math	math	PROPN
ma-154	109	3	.	.	PUNCT
ma-154	110	1	anal	anal	PROPN
ma-154	110	2	.	.	PUNCT
ma-154	111	1	10.28924	10.28924	NUM
ma-154	111	2	/	/	SYM
ma-154	111	3	ada	ada	PROPN
ma-154	111	4	/	/	SYM
ma-154	111	5	ma.3.15	ma.3.15	NOUN
ma-154	111	6	6	6	NUM
ma-154	111	7	where	where	SCONJ
ma-154	111	8	k̄	k̄	ADV
ma-154	111	9	=	=	SYM
ma-154	111	10	1	1	NUM
ma-154	111	11	8(4l0	8(4l0	NUM
ma-154	111	12	+	+	CCONJ
ma-154	111	13	√	√	NUM
ma-154	111	14	kl0	kl0	VERB
ma-154	111	15	+	+	NUM
ma-154	111	16	8l20	8l20	NUM
ma-154	111	17	+	+	CCONJ
ma-154	111	18	√	√	PROPN
ma-154	111	19	l0k	l0k	NOUN
ma-154	111	20	)	)	PUNCT
ma-154	111	21	.	.	PUNCT
ma-154	112	1	this	this	DET
ma-154	112	2	criterion	criterion	NOUN
ma-154	112	3	was	be	AUX
ma-154	112	4	given	give	VERB
ma-154	112	5	by	by	ADP
ma-154	112	6	us	we	PRON
ma-154	112	7	in	in	ADP
ma-154	112	8	[	[	X
ma-154	112	9	4	4	NUM
ma-154	112	10	]	]	PUNCT
ma-154	112	11	for	for	ADP
ma-154	112	12	k	k	PROPN
ma-154	112	13	=	=	PUNCT
ma-154	112	14	l−	l−	NOUN
ma-154	112	15	2	2	NUM
ma-154	112	16	.	.	X
ma-154	112	17	notice	notice	VERB
ma-154	112	18	that	that	SCONJ
ma-154	112	19	h	h	NOUN
ma-154	112	20	≤	≤	NOUN
ma-154	112	21	1	1	NUM
ma-154	112	22	2	2	NUM
ma-154	112	23	⇒	⇒	NOUN
ma-154	112	24	ha	ha	INTJ
ma-154	112	25	≤	≤	NUM
ma-154	112	26	1	1	NUM
ma-154	112	27	2	2	NUM
ma-154	112	28	.	.	PUNCT
ma-154	113	1	(	(	PUNCT
ma-154	113	2	2.26	2.26	NUM
ma-154	113	3	)	)	PUNCT
ma-154	113	4	hence	hence	ADV
ma-154	113	5	,	,	PUNCT
ma-154	113	6	if	if	SCONJ
ma-154	113	7	(	(	PUNCT
ma-154	113	8	2.25	2.25	NUM
ma-154	113	9	)	)	PUNCT
ma-154	113	10	and	and	CCONJ
ma-154	113	11	{	{	PUNCT
ma-154	113	12	rn	rn	NOUN
ma-154	113	13	}	}	PUNCT
ma-154	113	14	replace	replace	NOUN
ma-154	113	15	(	(	PUNCT
ma-154	113	16	2.17	2.17	NUM
ma-154	113	17	)	)	PUNCT
ma-154	113	18	and	and	CCONJ
ma-154	113	19	{	{	PUNCT
ma-154	113	20	sn	sn	PROPN
ma-154	113	21	}	}	PUNCT
ma-154	113	22	the	the	DET
ma-154	113	23	conclusions	conclusion	NOUN
ma-154	113	24	of	of	ADP
ma-154	113	25	theorem	theorem	ADJ
ma-154	113	26	2.7	2.7	NUM
ma-154	113	27	hold	hold	NOUN
ma-154	113	28	with	with	ADP
ma-154	113	29	these	these	DET
ma-154	113	30	changes	change	NOUN
ma-154	113	31	too	too	ADV
ma-154	113	32	.	.	PUNCT
ma-154	114	1	(	(	PUNCT
ma-154	114	2	iii)suppose	iii)suppose	ADP
ma-154	114	3	that	that	SCONJ
ma-154	114	4	there	there	PRON
ma-154	114	5	exist	exist	VERB
ma-154	114	6	a	a	DET
ma-154	114	7	>	>	X
ma-154	114	8	0	0	NUM
ma-154	114	9	,	,	PUNCT
ma-154	114	10	b	b	X
ma-154	114	11	>	>	X
ma-154	114	12	0	0	NUM
ma-154	114	13	such	such	ADJ
ma-154	114	14	that	that	SCONJ
ma-154	114	15	‖f	‖f	DET
ma-154	114	16	′(x0	′(x0	NOUN
ma-154	114	17	+	+	CCONJ
ma-154	114	18	θ(x1	θ(x1	ADJ
ma-154	114	19	−	−	PROPN
ma-154	114	20	x0))−	x0))−	NOUN
ma-154	115	1	f	f	PROPN
ma-154	116	1	′(x0)‖	′(x0)‖	NOUN
ma-154	116	2	≤	≤	NUM
ma-154	116	3	τa‖x1	τa‖x1	ADP
ma-154	116	4	−	−	PROPN
ma-154	117	1	x0‖	x0‖	PROPN
ma-154	117	2	(	(	PUNCT
ma-154	117	3	2.27	2.27	NUM
ma-154	117	4	)	)	PUNCT
ma-154	117	5	and	and	CCONJ
ma-154	117	6	‖f	‖f	ADJ
ma-154	117	7	′(x1)−	′(x1)−	NOUN
ma-154	117	8	f	f	NOUN
ma-154	117	9	′(x0)‖	′(x0)‖	NOUN
ma-154	117	10	≤	≤	NUM
ma-154	117	11	b‖x1	b‖x1	NOUN
ma-154	117	12	−	−	PROPN
ma-154	117	13	x0‖	x0‖	PROPN
ma-154	117	14	(	(	PUNCT
ma-154	117	15	2.28	2.28	NUM
ma-154	117	16	)	)	PUNCT
ma-154	117	17	for	for	ADP
ma-154	117	18	all	all	DET
ma-154	117	19	τ	τ	PRON
ma-154	117	20	∈	∈	PROPN
ma-154	118	1	[	[	X
ma-154	118	2	0	0	NUM
ma-154	118	3	,	,	PUNCT
ma-154	118	4	1	1	NUM
ma-154	118	5	]	]	PUNCT
ma-154	118	6	.	.	PUNCT
ma-154	119	1	then	then	ADV
ma-154	119	2	,	,	PUNCT
ma-154	119	3	it	it	PRON
ma-154	119	4	was	be	AUX
ma-154	119	5	shown	show	VERB
ma-154	119	6	in	in	ADP
ma-154	119	7	[	[	X
ma-154	119	8	5	5	NUM
ma-154	119	9	]	]	PUNCT
ma-154	119	10	that	that	DET
ma-154	119	11	sequence	sequence	NOUN
ma-154	119	12	{	{	PUNCT
ma-154	119	13	qn	qn	NOUN
ma-154	119	14	}	}	PUNCT
ma-154	119	15	defined	define	VERB
ma-154	119	16	by	by	ADP
ma-154	119	17	q0	q0	PROPN
ma-154	119	18	=	=	SYM
ma-154	119	19	0	0	NUM
ma-154	119	20	,	,	PUNCT
ma-154	119	21	q1	q1	NOUN
ma-154	119	22	=	=	SYM
ma-154	119	23	λ	λ	PROPN
ma-154	119	24	,	,	PUNCT
ma-154	119	25	q2	q2	NOUN
ma-154	119	26	=	=	PROPN
ma-154	119	27	q1	q1	PROPN
ma-154	119	28	+	+	CCONJ
ma-154	119	29	αa(q1	αa(q1	NUM
ma-154	119	30	−	−	NOUN
ma-154	119	31	q0)2	q0)2	NOUN
ma-154	119	32	2(1−	2(1−	NUM
ma-154	119	33	bαq1	bαq1	NOUN
ma-154	119	34	)	)	PUNCT
ma-154	119	35	,	,	PUNCT
ma-154	119	36	qn+2	qn+2	X
ma-154	120	1	=	=	SYM
ma-154	120	2	qn+1	qn+1	PROPN
ma-154	120	3	+	+	CCONJ
ma-154	120	4	kα(qn+1	kα(qn+1	PROPN
ma-154	120	5	−	−	PROPN
ma-154	120	6	qn)2	qn)2	PROPN
ma-154	120	7	2(1−	2(1−	NUM
ma-154	120	8	l0αqn+1	l0αqn+1	NOUN
ma-154	120	9	)	)	PUNCT
ma-154	120	10	is	be	AUX
ma-154	120	11	also	also	ADV
ma-154	120	12	majorizing	majorize	VERB
ma-154	120	13	for	for	ADP
ma-154	120	14	sequence	sequence	NOUN
ma-154	120	15	{	{	PUNCT
ma-154	120	16	xn	xn	NUM
ma-154	120	17	}	}	PUNCT
ma-154	120	18	.	.	PUNCT
ma-154	121	1	the	the	DET
ma-154	121	2	convergence	convergence	NOUN
ma-154	121	3	criterion	criterion	NOUN
ma-154	121	4	for	for	ADP
ma-154	121	5	sequence	sequence	NOUN
ma-154	121	6	{	{	PUNCT
ma-154	121	7	qn	qn	NOUN
ma-154	121	8	}	}	PUNCT
ma-154	121	9	is	be	AUX
ma-154	121	10	given	give	VERB
ma-154	121	11	by	by	ADP
ma-154	121	12	haa	haa	PROPN
ma-154	121	13	=	=	SYM
ma-154	121	14	λ	λ	NOUN
ma-154	121	15	2c	2c	NOUN
ma-154	121	16	≤	≤	NUM
ma-154	121	17	1	1	NUM
ma-154	121	18	2	2	NUM
ma-154	121	19	,	,	PUNCT
ma-154	121	20	(	(	PUNCT
ma-154	121	21	2.29	2.29	NUM
ma-154	121	22	)	)	PUNCT
ma-154	121	23	where	where	SCONJ
ma-154	121	24	p1(s	p1(s	NOUN
ma-154	121	25	)	)	PUNCT
ma-154	121	26	=	=	SYM
ma-154	121	27	(	(	PUNCT
ma-154	121	28	ka	ka	PROPN
ma-154	122	1	+	+	CCONJ
ma-154	122	2	2dl0(a	2dl0(a	NUM
ma-154	123	1	−	−	NUM
ma-154	123	2	2b))s2	2b))s2	NUM
ma-154	123	3	+	+	CCONJ
ma-154	123	4	4p(l0	4p(l0	NUM
ma-154	123	5	+	+	CCONJ
ma-154	123	6	b)s	b)s	X
ma-154	123	7	−	−	PRON
ma-154	123	8	4d	4d	NOUN
ma-154	123	9	,	,	PUNCT
ma-154	123	10	d	d	X
ma-154	123	11	=	=	SYM
ma-154	123	12	2k	2k	PROPN
ma-154	124	1	k	k	NOUN
ma-154	124	2	+	+	CCONJ
ma-154	124	3	√	√	PROPN
ma-154	124	4	k2	k2	NOUN
ma-154	124	5	+	+	CCONJ
ma-154	124	6	8l0k	8l0k	NUM
ma-154	124	7	,	,	PUNCT
ma-154	124	8	and	and	CCONJ
ma-154	124	9	c	c	X
ma-154	124	10	=	=	SYM
ma-154	124	11			PROPN
ma-154	124	12	1	1	NUM
ma-154	124	13	l0+b	l0+b	NOUN
ma-154	124	14	,	,	PUNCT
ma-154	124	15	ka	ka	PROPN
ma-154	125	1	+	+	CCONJ
ma-154	125	2	2dl0(a	2dl0(a	NUM
ma-154	125	3	−	−	NOUN
ma-154	125	4	2b	2b	NUM
ma-154	125	5	)	)	PUNCT
ma-154	125	6	=	=	SYM
ma-154	125	7	0positive	0positive	NUM
ma-154	125	8	root	root	NOUN
ma-154	125	9	of	of	ADP
ma-154	125	10	p1	p1	PROPN
ma-154	125	11	,	,	PUNCT
ma-154	125	12	ka	ka	PROPN
ma-154	126	1	+	+	CCONJ
ma-154	126	2	2dl0(a	2dl0(a	NUM
ma-154	126	3	−	−	NOUN
ma-154	126	4	2b	2b	NUM
ma-154	126	5	)	)	PUNCT
ma-154	126	6	>	>	X
ma-154	127	1	0smaller	0smaller	NUM
ma-154	127	2	positive	positive	ADJ
ma-154	127	3	root	root	NOUN
ma-154	127	4	of	of	ADP
ma-154	127	5	p1	p1	PROPN
ma-154	127	6	,	,	PUNCT
ma-154	127	7	ka	ka	PROPN
ma-154	128	1	+	+	CCONJ
ma-154	128	2	2dl0(a	2dl0(a	NUM
ma-154	128	3	−	−	NOUN
ma-154	128	4	2b	2b	NOUN
ma-154	128	5	)	)	PUNCT
ma-154	128	6	<	<	X
ma-154	128	7	0	0	X
ma-154	128	8	.	.	PUNCT
ma-154	128	9	notice	notice	VERB
ma-154	128	10	that	that	SCONJ
ma-154	129	1	b	b	X
ma-154	129	2	≤	≤	PRON
ma-154	129	3	a	a	DET
ma-154	129	4	≤	≤	NUM
ma-154	129	5	l0	l0	NOUN
ma-154	129	6	.	.	PUNCT
ma-154	130	1	hence	hence	ADV
ma-154	130	2	,	,	PUNCT
ma-154	130	3	{	{	PUNCT
ma-154	130	4	qn	qn	NOUN
ma-154	130	5	}	}	PUNCT
ma-154	130	6	is	be	AUX
ma-154	130	7	a	a	DET
ma-154	130	8	tighter	tight	ADJ
ma-154	130	9	majorizing	majorize	VERB
ma-154	130	10	sequence	sequence	NOUN
ma-154	130	11	than	than	ADP
ma-154	130	12	{	{	PUNCT
ma-154	130	13	rn	rn	NOUN
ma-154	130	14	}	}	PUNCT
ma-154	130	15	.	.	PUNCT
ma-154	131	1	criterion	criterion	NOUN
ma-154	131	2	(	(	PUNCT
ma-154	131	3	2.29	2.29	NUM
ma-154	131	4	)	)	PUNCT
ma-154	131	5	was	be	AUX
ma-154	131	6	given	give	VERB
ma-154	131	7	by	by	ADP
ma-154	131	8	us	we	PRON
ma-154	131	9	in	in	ADP
ma-154	131	10	[	[	X
ma-154	131	11	4	4	NUM
ma-154	131	12	]	]	PUNCT
ma-154	131	13	for	for	ADP
ma-154	131	14	k	k	NOUN
ma-154	131	15	=	=	SYM
ma-154	131	16	l2	l2	NOUN
ma-154	131	17	.	.	PUNCT
ma-154	132	1	therefore	therefore	ADV
ma-154	132	2	(	(	PUNCT
ma-154	132	3	2.29	2.29	NUM
ma-154	132	4	)	)	PUNCT
ma-154	132	5	and	and	CCONJ
ma-154	132	6	{	{	PUNCT
ma-154	132	7	qn	qn	NOUN
ma-154	132	8	}	}	PUNCT
ma-154	132	9	can	can	AUX
ma-154	132	10	also	also	ADV
ma-154	132	11	replace	replace	VERB
ma-154	132	12	(	(	PUNCT
ma-154	132	13	2.17	2.17	NUM
ma-154	132	14	)	)	PUNCT
ma-154	132	15	and	and	CCONJ
ma-154	132	16	{	{	PUNCT
ma-154	132	17	sn	sn	NOUN
ma-154	132	18	}	}	PUNCT
ma-154	132	19	in	in	ADP
ma-154	132	20	theorem	theorem	ADJ
ma-154	132	21	2.7	2.7	NUM
ma-154	132	22	.	.	PUNCT
ma-154	133	1	(	(	PUNCT
ma-154	133	2	iv	iv	X
ma-154	133	3	)	)	PUNCT
ma-154	133	4	it	it	PRON
ma-154	133	5	follows	follow	VERB
ma-154	133	6	from	from	ADP
ma-154	133	7	the	the	DET
ma-154	133	8	definition	definition	NOUN
ma-154	133	9	of	of	ADP
ma-154	133	10	sequence	sequence	NOUN
ma-154	133	11	{	{	PUNCT
ma-154	133	12	sn	sn	NOUN
ma-154	133	13	}	}	PUNCT
ma-154	133	14	that	that	SCONJ
ma-154	133	15	if	if	SCONJ
ma-154	133	16	l0αsn	l0αsn	PROPN
ma-154	133	17	<	<	X
ma-154	133	18	1	1	NUM
ma-154	133	19	.	.	PUNCT
ma-154	133	20	(	(	PUNCT
ma-154	133	21	2.30	2.30	NUM
ma-154	133	22	)	)	PUNCT
ma-154	133	23	then	then	ADV
ma-154	133	24	,	,	PUNCT
ma-154	133	25	sequence	sequence	NOUN
ma-154	133	26	{	{	PUNCT
ma-154	133	27	sn	sn	NOUN
ma-154	133	28	}	}	PUNCT
ma-154	133	29	is	be	AUX
ma-154	133	30	such	such	ADJ
ma-154	133	31	that	that	SCONJ
ma-154	133	32	0	0	NUM
ma-154	133	33	≤	≤	NUM
ma-154	133	34	sn	sn	PROPN
ma-154	133	35	≤	≤	NOUN
ma-154	133	36	sn+1	sn+1	VERB
ma-154	133	37	and	and	CCONJ
ma-154	133	38	limn−→∞	limn−→∞	PROPN
ma-154	133	39	sn	sn	PROPN
ma-154	133	40	=	=	PRON
ma-154	133	41	s∗	s∗	PROPN
ma-154	133	42	≤	≤	NUM
ma-154	133	43	1	1	NUM
ma-154	133	44	l0α	l0α	NOUN
ma-154	133	45	.	.	PUNCT
ma-154	134	1	hence	hence	ADV
ma-154	134	2	,	,	PUNCT
ma-154	134	3	weaker	weak	ADJ
ma-154	134	4	than	than	ADP
ma-154	134	5	all	all	DET
ma-154	134	6	conditions	condition	NOUN
ma-154	134	7	(	(	PUNCT
ma-154	134	8	2.30	2.30	NUM
ma-154	134	9	)	)	PUNCT
ma-154	134	10	can	can	AUX
ma-154	134	11	be	be	AUX
ma-154	134	12	used	use	VERB
ma-154	134	13	in	in	ADP
ma-154	134	14	theorem	theorem	ADJ
ma-154	134	15	2.7	2.7	NUM
ma-154	134	16	.	.	PUNCT
ma-154	135	1	https://doi.org/10.28924/ada/ma.3.15	https://doi.org/10.28924/ada/ma.3.15	NOUN
ma-154	135	2	eur	eur	PROPN
ma-154	135	3	.	.	PUNCT
ma-154	136	1	j.	j.	PROPN
ma-154	136	2	math	math	PROPN
ma-154	136	3	.	.	PUNCT
ma-154	137	1	anal	anal	PROPN
ma-154	137	2	.	.	PUNCT
ma-154	138	1	10.28924	10.28924	NUM
ma-154	138	2	/	/	SYM
ma-154	138	3	ada	ada	PROPN
ma-154	138	4	/	/	SYM
ma-154	138	5	ma.3.15	ma.3.15	NOUN
ma-154	138	6	73	73	NUM
ma-154	138	7	.	.	PUNCT
ma-154	139	1	examples	example	NOUN
ma-154	139	2	we	we	PRON
ma-154	139	3	test	test	VERB
ma-154	139	4	the	the	DET
ma-154	139	5	convergence	convergence	NOUN
ma-154	139	6	criteria	criterion	NOUN
ma-154	139	7	.	.	PUNCT
ma-154	140	1	example	example	NOUN
ma-154	140	2	3.1	3.1	NUM
ma-154	140	3	.	.	PUNCT
ma-154	140	4	defined	define	VERB
ma-154	140	5	the	the	DET
ma-154	140	6	real	real	ADJ
ma-154	140	7	function	function	NOUN
ma-154	140	8	f	f	PROPN
ma-154	140	9	on	on	ADP
ma-154	140	10	ω	ω	PROPN
ma-154	140	11	=	=	SYM
ma-154	140	12	b[x0	b[x0	PROPN
ma-154	140	13	,	,	PUNCT
ma-154	140	14	1−	1−	NUM
ma-154	140	15	δ	δ	X
ma-154	140	16	]	]	X
ma-154	140	17	,	,	PUNCT
ma-154	140	18	x0	x0	PROPN
ma-154	140	19	=	=	SYM
ma-154	141	1	1	1	NUM
ma-154	141	2	,	,	PUNCT
ma-154	141	3	δ	δ	PROPN
ma-154	141	4	∈	∈	PROPN
ma-154	141	5	(	(	PUNCT
ma-154	141	6	0	0	NUM
ma-154	141	7	,	,	PUNCT
ma-154	141	8	12	12	NUM
ma-154	141	9	)	)	PUNCT
ma-154	141	10	by	by	ADP
ma-154	141	11	f	f	PROPN
ma-154	141	12	(	(	PUNCT
ma-154	141	13	s	s	NOUN
ma-154	141	14	)	)	PUNCT
ma-154	141	15	=	=	SYM
ma-154	141	16	s3	s3	PROPN
ma-154	141	17	−	−	PROPN
ma-154	141	18	δ	δ	PROPN
ma-154	141	19	.	.	PUNCT
ma-154	142	1	then	then	ADV
ma-154	142	2	,	,	PUNCT
ma-154	142	3	the	the	DET
ma-154	142	4	definitions	definition	NOUN
ma-154	142	5	are	be	AUX
ma-154	142	6	satisfied	satisfied	ADJ
ma-154	142	7	for	for	ADP
ma-154	142	8	λ	λ	X
ma-154	142	9	=	=	SYM
ma-154	142	10	1−δ	1−δ	NUM
ma-154	142	11	3	3	NUM
ma-154	142	12	,	,	PUNCT
ma-154	142	13	α	α	NOUN
ma-154	142	14	=	=	SYM
ma-154	142	15	1	1	NUM
ma-154	142	16	3	3	NUM
ma-154	142	17	,	,	PUNCT
ma-154	142	18	l0	l0	PROPN
ma-154	142	19	=	=	SYM
ma-154	142	20	3(3	3(3	NUM
ma-154	142	21	−	−	PROPN
ma-154	142	22	δ	δ	PROPN
ma-154	142	23	)	)	PUNCT
ma-154	142	24	,	,	PUNCT
ma-154	142	25	l2	l2	NOUN
ma-154	142	26	=	=	SYM
ma-154	142	27	6(2	6(2	NUM
ma-154	142	28	−	−	PROPN
ma-154	142	29	δ	δ	PROPN
ma-154	142	30	)	)	PUNCT
ma-154	142	31	,	,	PUNCT
ma-154	142	32	l1	l1	PROPN
ma-154	142	33	=	=	PUNCT
ma-154	143	1	6(1	6(1	PROPN
ma-154	143	2	+	+	CCONJ
ma-154	143	3	1	1	NUM
ma-154	143	4	3−δ	3−δ	NUM
ma-154	143	5	)	)	PUNCT
ma-154	143	6	,	,	PUNCT
ma-154	144	1	x1	x1	NOUN
ma-154	144	2	=	=	PUNCT
ma-154	145	1	2+δ	2+δ	NUM
ma-154	145	2	3	3	NUM
ma-154	145	3	,	,	PUNCT
ma-154	145	4	l	l	NOUN
ma-154	145	5	=	=	SYM
ma-154	145	6	5	5	NUM
ma-154	145	7	(	(	PUNCT
ma-154	145	8	4−δ	4−δ	PROPN
ma-154	145	9	3−δ	3−δ	NUM
ma-154	145	10	)	)	PUNCT
ma-154	145	11	3+δ	3+δ	NUM
ma-154	145	12	3	3	NUM
ma-154	145	13	(	(	PUNCT
ma-154	145	14	4−δ	4−δ	PROPN
ma-154	145	15	3−δ	3−δ	NUM
ma-154	145	16	)	)	PUNCT
ma-154	145	17	2	2	NUM
ma-154	145	18	,	,	PUNCT
ma-154	145	19	a	a	DET
ma-154	145	20	=	=	SYM
ma-154	145	21	b	b	NOUN
ma-154	145	22	=	=	SYM
ma-154	145	23	δ	δ	PROPN
ma-154	145	24	+	+	ADP
ma-154	145	25	5	5	NUM
ma-154	145	26	,	,	PUNCT
ma-154	145	27	k	k	NOUN
ma-154	145	28	=	=	PUNCT
ma-154	145	29	5h3+δ	5h3+δ	NUM
ma-154	145	30	3h2	3h2	NUM
ma-154	145	31	,	,	PUNCT
ma-154	145	32	and	and	CCONJ
ma-154	145	33	h	h	NOUN
ma-154	146	1	=	=	SYM
ma-154	146	2	δ+2	δ+2	PROPN
ma-154	146	3	3	3	NUM
ma-154	146	4	+	+	SYM
ma-154	146	5	3−(1−δ)(3−δ	3−(1−δ)(3−δ	NUM
ma-154	146	6	)	)	PUNCT
ma-154	146	7	3(1−δ	3(1−δ	NUM
ma-154	146	8	)	)	PUNCT
ma-154	146	9	.	.	PUNCT
ma-154	147	1	denote	denote	VERB
ma-154	147	2	by	by	ADP
ma-154	147	3	m1,m2,m3,m4	m1,m2,m3,m4	PROPN
ma-154	147	4	the	the	DET
ma-154	147	5	set	set	NOUN
ma-154	147	6	of	of	ADP
ma-154	147	7	values	value	NOUN
ma-154	147	8	δ	δ	PROPN
ma-154	147	9	∈	∈	PROPN
ma-154	147	10	(	(	PUNCT
ma-154	147	11	0	0	NUM
ma-154	147	12	,	,	PUNCT
ma-154	147	13	12	12	NUM
ma-154	147	14	)	)	PUNCT
ma-154	147	15	for	for	ADP
ma-154	147	16	which	which	PRON
ma-154	147	17	(	(	PUNCT
ma-154	147	18	2.20	2.20	NUM
ma-154	147	19	)	)	PUNCT
ma-154	147	20	,	,	PUNCT
ma-154	147	21	(	(	PUNCT
ma-154	147	22	2.17	2.17	NUM
ma-154	147	23	)	)	PUNCT
ma-154	147	24	,	,	PUNCT
ma-154	147	25	(	(	PUNCT
ma-154	147	26	2.25	2.25	NUM
ma-154	147	27	)	)	PUNCT
ma-154	147	28	and	and	CCONJ
ma-154	147	29	(	(	PUNCT
ma-154	147	30	2.29	2.29	NUM
ma-154	147	31	)	)	PUNCT
ma-154	147	32	are	be	AUX
ma-154	147	33	satisfied	satisfied	ADJ
ma-154	147	34	,	,	PUNCT
ma-154	147	35	respectively	respectively	ADV
ma-154	147	36	.	.	PUNCT
ma-154	148	1	then	then	ADV
ma-154	148	2	,	,	PUNCT
ma-154	148	3	by	by	ADP
ma-154	148	4	solving	solve	VERB
ma-154	148	5	these	these	DET
ma-154	148	6	inequalities	inequality	NOUN
ma-154	148	7	for	for	ADP
ma-154	148	8	δ	δ	PROPN
ma-154	148	9	,	,	PUNCT
ma-154	148	10	we	we	PRON
ma-154	148	11	get	get	VERB
ma-154	148	12	m1	m1	NOUN
ma-154	148	13	=	=	NOUN
ma-154	148	14	∅	∅	NOUN
ma-154	148	15	,	,	PUNCT
ma-154	148	16	m2	m2	PROPN
ma-154	148	17	=	=	PUNCT
ma-154	148	18	(	(	PUNCT
ma-154	148	19	0.0751	0.0751	NUM
ma-154	148	20	,	,	PUNCT
ma-154	148	21	0.5	0.5	NUM
ma-154	148	22	)	)	PUNCT
ma-154	148	23	,	,	PUNCT
ma-154	148	24	m3	m3	PROPN
ma-154	148	25	=	=	SYM
ma-154	148	26	(	(	PUNCT
ma-154	148	27	0.1320	0.1320	NUM
ma-154	148	28	,	,	PUNCT
ma-154	148	29	0.5	0.5	NUM
ma-154	148	30	)	)	PUNCT
ma-154	148	31	and	and	CCONJ
ma-154	148	32	m4	m4	PROPN
ma-154	148	33	=	=	SYM
ma-154	148	34	(	(	PUNCT
ma-154	148	35	0.3967	0.3967	NUM
ma-154	148	36	,	,	PUNCT
ma-154	148	37	0.5	0.5	NUM
ma-154	148	38	)	)	PUNCT
ma-154	148	39	.	.	PUNCT
ma-154	149	1	notice	notice	NOUN
ma-154	149	2	in	in	ADP
ma-154	149	3	particular	particular	ADJ
ma-154	149	4	that	that	SCONJ
ma-154	149	5	the	the	DET
ma-154	149	6	newton	newton	PROPN
ma-154	149	7	-	-	PUNCT
ma-154	149	8	kantorovich	kantorovich	PROPN
ma-154	149	9	criterion	criterion	NOUN
ma-154	149	10	(	(	PUNCT
ma-154	149	11	2.20	2.20	NUM
ma-154	149	12	)	)	PUNCT
ma-154	149	13	[	[	X
ma-154	149	14	1	1	NUM
ma-154	149	15	,	,	PUNCT
ma-154	149	16	9–15	9–15	PROPN
ma-154	149	17	]	]	PUNCT
ma-154	149	18	can	can	AUX
ma-154	149	19	not	not	PART
ma-154	149	20	assure	assure	VERB
ma-154	149	21	convergence	convergence	NOUN
ma-154	149	22	of	of	ADP
ma-154	149	23	nm	nm	NOUN
ma-154	149	24	since	since	SCONJ
ma-154	149	25	m1	m1	PROPN
ma-154	149	26	=	=	PUNCT
ma-154	149	27	∅.	∅.	VERB
ma-154	149	28	a	a	DET
ma-154	149	29	second	second	ADJ
ma-154	149	30	example	example	NOUN
ma-154	149	31	is	be	AUX
ma-154	149	32	provided	provide	VERB
ma-154	149	33	to	to	PART
ma-154	149	34	show	show	VERB
ma-154	149	35	that	that	SCONJ
ma-154	149	36	our	our	PRON
ma-154	149	37	conditions	condition	NOUN
ma-154	149	38	can	can	AUX
ma-154	149	39	be	be	AUX
ma-154	149	40	used	use	VERB
ma-154	149	41	to	to	PART
ma-154	149	42	solve	solve	VERB
ma-154	149	43	equations	equation	NOUN
ma-154	149	44	incases	incase	NOUN
ma-154	149	45	where	where	SCONJ
ma-154	149	46	the	the	DET
ma-154	149	47	ones	one	NOUN
ma-154	149	48	in	in	ADP
ma-154	149	49	[	[	X
ma-154	149	50	1	1	NUM
ma-154	149	51	,	,	PUNCT
ma-154	149	52	2	2	NUM
ma-154	149	53	,	,	PUNCT
ma-154	149	54	10,12,13	10,12,13	NUM
ma-154	149	55	]	]	PUNCT
ma-154	149	56	can	can	AUX
ma-154	149	57	not	not	PART
ma-154	149	58	.	.	PUNCT
ma-154	150	1	example	example	NOUN
ma-154	150	2	3.2	3.2	NUM
ma-154	150	3	.	.	PUNCT
ma-154	151	1	consider	consider	VERB
ma-154	151	2	e1	e1	NOUN
ma-154	151	3	=	=	SYM
ma-154	151	4	e2	e2	PROPN
ma-154	151	5	=	=	PUNCT
ma-154	151	6	c[0	c[0	PROPN
ma-154	151	7	,	,	PUNCT
ma-154	151	8	1	1	NUM
ma-154	151	9	]	]	PUNCT
ma-154	151	10	with	with	ADP
ma-154	151	11	the	the	DET
ma-154	151	12	norm	norm	NOUN
ma-154	151	13	-	-	PUNCT
ma-154	151	14	max	max	NOUN
ma-154	151	15	.	.	PUNCT
ma-154	152	1	set	set	VERB
ma-154	152	2	ω	ω	PROPN
ma-154	152	3	=	=	PROPN
ma-154	152	4	b(x0	b(x0	NOUN
ma-154	152	5	,	,	PUNCT
ma-154	152	6	3	3	NUM
ma-154	152	7	)	)	PUNCT
ma-154	152	8	.	.	PUNCT
ma-154	153	1	define	define	NOUN
ma-154	153	2	,	,	PUNCT
ma-154	153	3	hammerstein	hammerstein	NOUN
ma-154	153	4	-	-	PUNCT
ma-154	153	5	type	type	NOUN
ma-154	153	6	integral	integral	ADJ
ma-154	153	7	operator	operator	NOUN
ma-154	153	8	m	m	PRON
ma-154	153	9	on	on	ADP
ma-154	153	10	ω	ω	NUM
ma-154	153	11	by	by	ADP
ma-154	153	12	m(z)(w	m(z)(w	NOUN
ma-154	153	13	)	)	PUNCT
ma-154	153	14	=	=	SYM
ma-154	154	1	z(w)−	z(w)−	PROPN
ma-154	154	2	y(w)−	y(w)−	PROPN
ma-154	154	3	∫	∫	PROPN
ma-154	154	4	1	1	NUM
ma-154	154	5	0	0	NUM
ma-154	154	6	t	t	PROPN
ma-154	154	7	(	(	PUNCT
ma-154	154	8	w	w	NOUN
ma-154	154	9	,	,	PUNCT
ma-154	154	10	t)v3(t)dt	t)v3(t)dt	ADJ
ma-154	154	11	,	,	PUNCT
ma-154	154	12	(	(	PUNCT
ma-154	154	13	3.1	3.1	NUM
ma-154	154	14	)	)	PUNCT
ma-154	154	15	w	w	NOUN
ma-154	154	16	∈	∈	PROPN
ma-154	155	1	[	[	X
ma-154	155	2	0	0	NUM
ma-154	155	3	,	,	PUNCT
ma-154	155	4	1	1	NUM
ma-154	155	5	]	]	PUNCT
ma-154	155	6	,	,	PUNCT
ma-154	155	7	z	z	PROPN
ma-154	155	8	∈	∈	PROPN
ma-154	155	9	c[0	c[0	PROPN
ma-154	155	10	,	,	PUNCT
ma-154	155	11	1	1	NUM
ma-154	155	12	]	]	PUNCT
ma-154	155	13	,	,	PUNCT
ma-154	155	14	where	where	SCONJ
ma-154	155	15	y	y	PROPN
ma-154	155	16	∈	∈	PROPN
ma-154	155	17	c[0	c[0	PROPN
ma-154	155	18	,	,	PUNCT
ma-154	155	19	1	1	NUM
ma-154	155	20	]	]	PUNCT
ma-154	155	21	is	be	AUX
ma-154	155	22	fixed	fix	VERB
ma-154	155	23	and	and	CCONJ
ma-154	155	24	t	t	PROPN
ma-154	155	25	is	be	AUX
ma-154	155	26	a	a	DET
ma-154	155	27	green	green	PROPN
ma-154	155	28	’s	’s	PART
ma-154	155	29	kernel	kernel	NOUN
ma-154	155	30	defined	define	VERB
ma-154	155	31	by	by	ADP
ma-154	155	32	t	t	PROPN
ma-154	155	33	(	(	PUNCT
ma-154	155	34	w	w	PROPN
ma-154	155	35	,	,	PUNCT
ma-154	155	36	u	u	NOUN
ma-154	155	37	)	)	PUNCT
ma-154	155	38	=	=	SYM
ma-154	155	39	{	{	PUNCT
ma-154	155	40	(	(	PUNCT
ma-154	155	41	1−	1−	NUM
ma-154	155	42	w)u	w)u	NOUN
ma-154	155	43	,	,	PUNCT
ma-154	155	44	i	i	PRON
ma-154	155	45	f	f	NOUN
ma-154	155	46	u	u	X
ma-154	155	47	≤	≤	X
ma-154	155	48	w	w	PROPN
ma-154	155	49	w(1−	w(1−	PROPN
ma-154	155	50	u	u	PROPN
ma-154	155	51	)	)	PUNCT
ma-154	155	52	,	,	PUNCT
ma-154	156	1	i	i	PRON
ma-154	156	2	f	f	PROPN
ma-154	156	3	w	w	PROPN
ma-154	156	4	≤	≤	PROPN
ma-154	156	5	u.	u.	NOUN
ma-154	156	6	(	(	PUNCT
ma-154	156	7	3.2	3.2	NUM
ma-154	156	8	)	)	PUNCT
ma-154	156	9	then	then	ADV
ma-154	156	10	,	,	PUNCT
ma-154	156	11	the	the	DET
ma-154	156	12	derivative	derivative	NOUN
ma-154	156	13	m	m	VERB
ma-154	156	14	′	′	NUM
ma-154	156	15	according	accord	VERB
ma-154	156	16	to	to	ADP
ma-154	156	17	fréchet	fréchet	PROPN
ma-154	156	18	is	be	AUX
ma-154	156	19	defined	define	VERB
ma-154	156	20	by	by	ADP
ma-154	156	21	[	[	X
ma-154	156	22	m	m	NOUN
ma-154	156	23	′(v)(z)](w	′(v)(z)](w	PROPN
ma-154	156	24	)	)	PUNCT
ma-154	157	1	=	=	PRON
ma-154	157	2	z(w)−	z(w)−	PROPN
ma-154	157	3	3	3	NUM
ma-154	157	4	∫	∫	PROPN
ma-154	157	5	1	1	NUM
ma-154	157	6	0	0	NUM
ma-154	157	7	t	t	PROPN
ma-154	157	8	(	(	PUNCT
ma-154	157	9	w	w	PROPN
ma-154	157	10	,	,	PUNCT
ma-154	157	11	u)v2(t)z(t)dt	u)v2(t)z(t)dt	NOUN
ma-154	157	12	,	,	PUNCT
ma-154	157	13	(	(	PUNCT
ma-154	157	14	3.3	3.3	NUM
ma-154	157	15	)	)	PUNCT
ma-154	157	16	w	w	NOUN
ma-154	157	17	∈	∈	PROPN
ma-154	158	1	[	[	X
ma-154	158	2	0	0	NUM
ma-154	158	3	,	,	PUNCT
ma-154	158	4	1	1	NUM
ma-154	158	5	]	]	PUNCT
ma-154	158	6	,	,	PUNCT
ma-154	158	7	z	z	PROPN
ma-154	158	8	∈	∈	PROPN
ma-154	158	9	c[0	c[0	PROPN
ma-154	158	10	,	,	PUNCT
ma-154	158	11	1	1	NUM
ma-154	158	12	]	]	PUNCT
ma-154	158	13	.	.	PUNCT
ma-154	159	1	let	let	VERB
ma-154	159	2	y(w	y(w	NOUN
ma-154	159	3	)	)	PUNCT
ma-154	159	4	=	=	SYM
ma-154	160	1	x0(w	x0(w	PROPN
ma-154	160	2	)	)	PUNCT
ma-154	160	3	=	=	SYM
ma-154	161	1	1	1	X
ma-154	161	2	.	.	PUNCT
ma-154	161	3	then	then	ADV
ma-154	161	4	,	,	PUNCT
ma-154	161	5	using	use	VERB
ma-154	161	6	(	(	PUNCT
ma-154	161	7	3.1)-(3.3	3.1)-(3.3	NUM
ma-154	161	8	)	)	PUNCT
ma-154	161	9	,	,	PUNCT
ma-154	161	10	we	we	PRON
ma-154	161	11	obtain	obtain	VERB
ma-154	161	12	m	m	VERB
ma-154	161	13	′(x0)−1	′(x0)−1	NOUN
ma-154	161	14	∈	∈	PROPN
ma-154	161	15	l(e2	l(e2	NOUN
ma-154	161	16	,	,	PUNCT
ma-154	161	17	e1	e1	PROPN
ma-154	161	18	)	)	PUNCT
ma-154	161	19	,	,	PUNCT
ma-154	161	20	‖i	‖i	NOUN
ma-154	161	21	−	−	NOUN
ma-154	161	22	m	m	VERB
ma-154	162	1	′(x0)‖	′(x0)‖	NOUN
ma-154	162	2	<	<	X
ma-154	162	3	3	3	NUM
ma-154	162	4	8	8	NUM
ma-154	162	5	,	,	PUNCT
ma-154	162	6	‖m	‖m	NOUN
ma-154	162	7	′(x0	′(x0	NOUN
ma-154	162	8	)	)	PUNCT
ma-154	162	9	−1‖	−1‖	PUNCT
ma-154	163	1	≤	≤	NUM
ma-154	163	2	8	8	NUM
ma-154	163	3	5	5	NUM
ma-154	163	4	:	:	PUNCT
ma-154	163	5	=	=	SYM
ma-154	163	6	α	α	NOUN
ma-154	163	7	,	,	PUNCT
ma-154	163	8	λ	λ	X
ma-154	163	9	=	=	NOUN
ma-154	163	10	1	1	NUM
ma-154	163	11	5	5	NUM
ma-154	163	12	,	,	PUNCT
ma-154	163	13	l0	l0	NOUN
ma-154	163	14	=	=	NOUN
ma-154	163	15	12	12	NUM
ma-154	163	16	5	5	NUM
ma-154	163	17	,	,	PUNCT
ma-154	163	18	l2	l2	NOUN
ma-154	163	19	=	=	SYM
ma-154	163	20	18	18	NUM
ma-154	163	21	5	5	NUM
ma-154	163	22	,	,	PUNCT
ma-154	163	23	and	and	CCONJ
ma-154	163	24	ω0	ω0	ADV
ma-154	163	25	=	=	SYM
ma-154	163	26	b(1	b(1	PROPN
ma-154	163	27	,	,	PUNCT
ma-154	163	28	3	3	NUM
ma-154	163	29	)	)	PUNCT
ma-154	163	30	∩	∩	ADJ
ma-154	163	31	b(1	b(1	PROPN
ma-154	163	32	,	,	PUNCT
ma-154	163	33	512	512	NUM
ma-154	163	34	)	)	PUNCT
ma-154	163	35	=	=	SYM
ma-154	163	36	b(1	b(1	PROPN
ma-154	163	37	,	,	PUNCT
ma-154	163	38	512	512	NUM
ma-154	163	39	)	)	PUNCT
ma-154	163	40	,	,	PUNCT
ma-154	163	41	so	so	ADV
ma-154	163	42	l1	l1	PROPN
ma-154	163	43	=	=	PROPN
ma-154	163	44	3	3	NUM
ma-154	163	45	2	2	NUM
ma-154	163	46	,	,	PUNCT
ma-154	163	47	and	and	CCONJ
ma-154	163	48	l0	l0	NOUN
ma-154	163	49	<	<	X
ma-154	163	50	l2	l2	PROPN
ma-154	163	51	,	,	PUNCT
ma-154	163	52	l1	l1	PROPN
ma-154	163	53	<	<	X
ma-154	163	54	l2	l2	PROPN
ma-154	163	55	.	.	PUNCT
ma-154	164	1	set	set	VERB
ma-154	164	2	k	k	NOUN
ma-154	164	3	=	=	PUNCT
ma-154	164	4	l	l	NOUN
ma-154	164	5	=	=	SYM
ma-154	164	6	l1	l1	PROPN
ma-154	164	7	.	.	PUNCT
ma-154	165	1	then	then	ADV
ma-154	165	2	,	,	PUNCT
ma-154	165	3	the	the	DET
ma-154	165	4	old	old	ADJ
ma-154	165	5	sufficient	sufficient	ADJ
ma-154	165	6	convergence	convergence	NOUN
ma-154	165	7	criterion	criterion	NOUN
ma-154	165	8	is	be	AUX
ma-154	165	9	not	not	PART
ma-154	165	10	satisfied	satisfied	ADJ
ma-154	165	11	,	,	PUNCT
ma-154	165	12	since	since	SCONJ
ma-154	165	13	αλl2	αλl2	NOUN
ma-154	165	14	=	=	NOUN
ma-154	165	15	1	1	NUM
ma-154	165	16	5	5	NUM
ma-154	165	17	8	8	NUM
ma-154	165	18	5	5	NUM
ma-154	165	19	18	18	NUM
ma-154	165	20	5	5	NUM
ma-154	165	21	=	=	SYM
ma-154	165	22	144	144	NUM
ma-154	165	23	125	125	NUM
ma-154	165	24	>	>	SYM
ma-154	165	25	1	1	NUM
ma-154	165	26	2	2	NUM
ma-154	165	27	holds	hold	NOUN
ma-154	165	28	.	.	PUNCT
ma-154	166	1	therefore	therefore	ADV
ma-154	166	2	,	,	PUNCT
ma-154	166	3	there	there	PRON
ma-154	166	4	is	be	VERB
ma-154	166	5	no	no	DET
ma-154	166	6	guarantee	guarantee	NOUN
ma-154	166	7	that	that	SCONJ
ma-154	166	8	newton	newton	PROPN
ma-154	166	9	’s	’s	PART
ma-154	166	10	method	method	NOUN
ma-154	166	11	(	(	PUNCT
ma-154	166	12	1.2	1.2	NUM
ma-154	166	13	)	)	PUNCT
ma-154	166	14	converges	converge	NOUN
ma-154	166	15	to	to	ADP
ma-154	166	16	x∗	x∗	PROPN
ma-154	166	17	under	under	ADP
ma-154	166	18	the	the	DET
ma-154	166	19	conditions	condition	NOUN
ma-154	166	20	of	of	ADP
ma-154	166	21	the	the	DET
ma-154	166	22	aforementioned	aforementioned	ADJ
ma-154	166	23	references	reference	NOUN
ma-154	166	24	.	.	PUNCT
ma-154	167	1	but	but	CCONJ
ma-154	167	2	our	our	PRON
ma-154	167	3	condition	condition	NOUN
ma-154	167	4	hold	hold	VERB
ma-154	167	5	,	,	PUNCT
ma-154	167	6	since	since	SCONJ
ma-154	167	7	dba	dba	NOUN
ma-154	167	8	=	=	NOUN
ma-154	167	9	1	1	NUM
ma-154	167	10	5	5	NUM
ma-154	167	11	8	8	NUM
ma-154	167	12	5	5	NUM
ma-154	167	13	3	3	NUM
ma-154	167	14	2	2	NUM
ma-154	167	15	=	=	SYM
ma-154	167	16	24	24	NUM
ma-154	167	17	50	50	NUM
ma-154	167	18	<	<	SYM
ma-154	167	19	1	1	NUM
ma-154	167	20	2	2	NUM
ma-154	167	21	.	.	PUNCT
ma-154	168	1	therefore	therefore	ADV
ma-154	168	2	,	,	PUNCT
ma-154	168	3	the	the	DET
ma-154	168	4	conclusions	conclusion	NOUN
ma-154	168	5	of	of	ADP
ma-154	168	6	our	our	PRON
ma-154	168	7	theorem	theorem	ADJ
ma-154	168	8	2.7	2.7	NUM
ma-154	168	9	follow	follow	NOUN
ma-154	168	10	.	.	PUNCT
ma-154	169	1	https://doi.org/10.28924/ada/ma.3.15	https://doi.org/10.28924/ada/ma.3.15	NOUN
ma-154	169	2	eur	eur	PROPN
ma-154	169	3	.	.	PUNCT
ma-154	170	1	j.	j.	PROPN
ma-154	170	2	math	math	PROPN
ma-154	170	3	.	.	PUNCT
ma-154	171	1	anal	anal	PROPN
ma-154	171	2	.	.	PUNCT
ma-154	172	1	10.28924	10.28924	NUM
ma-154	172	2	/	/	SYM
ma-154	172	3	ada	ada	PROPN
ma-154	172	4	/	/	SYM
ma-154	172	5	ma.3.15	ma.3.15	NOUN
ma-154	172	6	84	84	NUM
ma-154	172	7	.	.	PUNCT
ma-154	173	1	conclusion	conclusion	VERB
ma-154	173	2	the	the	DET
ma-154	173	3	technique	technique	NOUN
ma-154	173	4	of	of	ADP
ma-154	173	5	recurrent	recurrent	ADJ
ma-154	173	6	functions	function	NOUN
ma-154	173	7	has	have	AUX
ma-154	173	8	been	be	AUX
ma-154	173	9	utilized	utilize	VERB
ma-154	173	10	to	to	PART
ma-154	173	11	extend	extend	VERB
ma-154	173	12	the	the	DET
ma-154	173	13	sufficient	sufficient	ADJ
ma-154	173	14	conditions	condition	NOUN
ma-154	173	15	forconvergence	forconvergence	NOUN
ma-154	173	16	of	of	ADP
ma-154	173	17	nm	nm	NOUN
ma-154	173	18	for	for	ADP
ma-154	173	19	solving	solve	VERB
ma-154	173	20	nonlinear	nonlinear	ADJ
ma-154	173	21	equations	equation	NOUN
ma-154	173	22	.	.	PUNCT
ma-154	174	1	the	the	DET
ma-154	174	2	new	new	ADJ
ma-154	174	3	results	result	NOUN
ma-154	174	4	are	be	AUX
ma-154	174	5	finer	fine	ADJ
ma-154	174	6	than	than	ADP
ma-154	174	7	the	the	DET
ma-154	174	8	earlierones	earlierone	NOUN
ma-154	174	9	.	.	PUNCT
ma-154	175	1	so	so	ADV
ma-154	175	2	,	,	PUNCT
ma-154	175	3	they	they	PRON
ma-154	175	4	can	can	AUX
ma-154	175	5	replace	replace	VERB
ma-154	175	6	them	they	PRON
ma-154	175	7	.	.	PUNCT
ma-154	176	1	no	no	DET
ma-154	176	2	additional	additional	ADJ
ma-154	176	3	conditions	condition	NOUN
ma-154	176	4	have	have	AUX
ma-154	176	5	been	be	AUX
ma-154	176	6	used	use	VERB
ma-154	176	7	.	.	PUNCT
ma-154	177	1	the	the	DET
ma-154	177	2	technique	technique	NOUN
ma-154	177	3	is	be	AUX
ma-154	177	4	verygeneral	verygeneral	ADJ
ma-154	177	5	rendering	rendering	NOUN
ma-154	177	6	useful	useful	ADJ
ma-154	177	7	to	to	PART
ma-154	177	8	extend	extend	VERB
ma-154	177	9	the	the	DET
ma-154	177	10	usage	usage	NOUN
ma-154	177	11	of	of	ADP
ma-154	177	12	other	other	ADJ
ma-154	177	13	iterative	iterative	NOUN
ma-154	177	14	methods	method	NOUN
ma-154	177	15	.	.	PUNCT
ma-154	178	1	declarations	declaration	NOUN
ma-154	178	2	the	the	DET
ma-154	178	3	authors	author	NOUN
ma-154	178	4	declare	declare	VERB
ma-154	178	5	that	that	SCONJ
ma-154	178	6	there	there	PRON
ma-154	178	7	are	be	VERB
ma-154	178	8	no	no	DET
ma-154	178	9	competing	compete	VERB
ma-154	178	10	interests	interest	NOUN
ma-154	178	11	and	and	CCONJ
ma-154	178	12	that	that	SCONJ
ma-154	178	13	all	all	DET
ma-154	178	14	authors	author	NOUN
ma-154	178	15	contributedequally	contributedequally	ADV
ma-154	178	16	in	in	ADP
ma-154	178	17	conceptualization	conceptualization	NOUN
ma-154	178	18	,	,	PUNCT
ma-154	178	19	methodology	methodology	NOUN
ma-154	178	20	,	,	PUNCT
ma-154	178	21	formal	formal	ADJ
ma-154	178	22	analysis	analysis	NOUN
ma-154	178	23	,	,	PUNCT
ma-154	178	24	and	and	CCONJ
ma-154	178	25	investigation	investigation	NOUN
ma-154	178	26	.	.	PUNCT
ma-154	179	1	the	the	DET
ma-154	179	2	original	original	ADJ
ma-154	179	3	draftwas	draftwas	NOUN
ma-154	179	4	prepared	prepare	VERB
ma-154	179	5	by	by	ADP
ma-154	179	6	i.	i.	PROPN
ma-154	179	7	k.	k.	PROPN
ma-154	179	8	argyros	argyros	PROPN
ma-154	179	9	and	and	CCONJ
ma-154	179	10	review	review	VERB
ma-154	179	11	and	and	CCONJ
ma-154	179	12	editing	editing	NOUN
ma-154	179	13	was	be	AUX
ma-154	179	14	done	do	VERB
ma-154	179	15	by	by	ADP
ma-154	179	16	s.	s.	PROPN
ma-154	179	17	regmi	regmi	PROPN
ma-154	179	18	,	,	PUNCT
ma-154	179	19	s.	s.	PROPN
ma-154	179	20	george	george	PROPN
ma-154	179	21	,	,	PUNCT
ma-154	179	22	and	and	CCONJ
ma-154	179	23	m.argyros	m.argyro	NOUN
ma-154	179	24	.	.	PUNCT
ma-154	180	1	references	reference	NOUN
ma-154	180	2	[	[	X
ma-154	180	3	1	1	NUM
ma-154	180	4	]	]	PUNCT
ma-154	180	5	s.	s.	PROPN
ma-154	180	6	adly	adly	PROPN
ma-154	180	7	,	,	PUNCT
ma-154	180	8	h.v	h.v	PROPN
ma-154	180	9	.	.	PROPN
ma-154	180	10	ngai	ngai	PROPN
ma-154	180	11	,	,	PUNCT
ma-154	180	12	v.v	v.v	PROPN
ma-154	180	13	.	.	PROPN
ma-154	180	14	nguyen	nguyen	PROPN
ma-154	180	15	,	,	PUNCT
ma-154	180	16	newton	newton	PROPN
ma-154	180	17	’s	’s	PART
ma-154	180	18	methods	method	NOUN
ma-154	180	19	for	for	ADP
ma-154	180	20	solving	solve	VERB
ma-154	180	21	generalized	generalized	ADJ
ma-154	180	22	equations	equation	NOUN
ma-154	180	23	:	:	PUNCT
ma-154	180	24	kantorovich	kantorovich	PROPN
ma-154	180	25	’s	’s	PART
ma-154	180	26	and	and	CCONJ
ma-154	180	27	smale’sapproaches	smale’sapproache	NOUN
ma-154	180	28	,	,	PUNCT
ma-154	180	29	j.	j.	PROPN
ma-154	180	30	math	math	PROPN
ma-154	180	31	.	.	PUNCT
ma-154	181	1	anal	anal	PROPN
ma-154	181	2	.	.	PUNCT
ma-154	182	1	appl	appl	PROPN
ma-154	182	2	.	.	PUNCT
ma-154	183	1	439	439	NUM
ma-154	183	2	(	(	PUNCT
ma-154	183	3	2016	2016	NUM
ma-154	183	4	)	)	PUNCT
ma-154	183	5	396	396	NUM
ma-154	183	6	-	-	SYM
ma-154	183	7	418	418	NUM
ma-154	183	8	.	.	PUNCT
ma-154	184	1	https://doi.org/10.1016/j.jmaa.2016.02.047.[2	https://doi.org/10.1016/j.jmaa.2016.02.047.[2	ADV
ma-154	184	2	]	]	PUNCT
ma-154	184	3	s.	s.	PROPN
ma-154	184	4	adly	adly	PROPN
ma-154	184	5	,	,	PUNCT
ma-154	184	6	r.	r.	PROPN
ma-154	184	7	cibulka	cibulka	PROPN
ma-154	184	8	,	,	PUNCT
ma-154	184	9	h.v	h.v	PROPN
ma-154	184	10	.	.	PROPN
ma-154	184	11	ngai	ngai	PROPN
ma-154	184	12	,	,	PUNCT
ma-154	184	13	newton	newton	PROPN
ma-154	184	14	’s	’s	PART
ma-154	184	15	method	method	NOUN
ma-154	184	16	for	for	ADP
ma-154	184	17	solving	solve	VERB
ma-154	184	18	inclusions	inclusion	NOUN
ma-154	184	19	using	use	VERB
ma-154	184	20	set	set	NOUN
ma-154	184	21	-	-	PUNCT
ma-154	184	22	valued	value	VERB
ma-154	184	23	approximations	approximation	NOUN
ma-154	184	24	,	,	PUNCT
ma-154	184	25	siam	siam	PROPN
ma-154	184	26	j.optim	j.optim	NOUN
ma-154	184	27	.	.	PUNCT
ma-154	185	1	25	25	NUM
ma-154	185	2	(	(	PUNCT
ma-154	185	3	2015	2015	NUM
ma-154	185	4	)	)	PUNCT
ma-154	185	5	159	159	NUM
ma-154	185	6	-	-	SYM
ma-154	185	7	184	184	NUM
ma-154	185	8	.	.	PUNCT
ma-154	186	1	https://doi.org/10.1137/130926730.[3	https://doi.org/10.1137/130926730.[3	PROPN
ma-154	186	2	]	]	X
ma-154	186	3	i.k	i.k	PROPN
ma-154	186	4	.	.	PROPN
ma-154	186	5	argyros	argyros	PROPN
ma-154	186	6	,	,	PUNCT
ma-154	186	7	unified	unified	ADJ
ma-154	186	8	convergence	convergence	NOUN
ma-154	186	9	criteria	criterion	NOUN
ma-154	186	10	for	for	ADP
ma-154	186	11	iterative	iterative	NOUN
ma-154	186	12	banach	banach	NOUN
ma-154	186	13	space	space	NOUN
ma-154	186	14	valued	value	VERB
ma-154	186	15	methods	method	NOUN
ma-154	186	16	with	with	ADP
ma-154	186	17	applications	application	NOUN
ma-154	186	18	,	,	PUNCT
ma-154	186	19	mathematics,9	mathematics,9	NOUN
ma-154	186	20	(	(	PUNCT
ma-154	186	21	2021	2021	NUM
ma-154	186	22	)	)	PUNCT
ma-154	186	23	1942	1942	NUM
ma-154	186	24	.	.	PUNCT
ma-154	187	1	https://doi.org/10.3390/math9161942.[4	https://doi.org/10.3390/math9161942.[4	PROPN
ma-154	187	2	]	]	PUNCT
ma-154	187	3	i.k	i.k	PROPN
ma-154	187	4	.	.	PROPN
ma-154	187	5	argyros	argyros	PROPN
ma-154	187	6	,	,	PUNCT
ma-154	187	7	s.	s.	PROPN
ma-154	187	8	hilout	hilout	PROPN
ma-154	187	9	,	,	PUNCT
ma-154	187	10	weaker	weak	ADJ
ma-154	187	11	conditions	condition	NOUN
ma-154	187	12	for	for	ADP
ma-154	187	13	the	the	DET
ma-154	187	14	convergence	convergence	NOUN
ma-154	187	15	of	of	ADP
ma-154	187	16	newton	newton	PROPN
ma-154	187	17	’s	’s	PART
ma-154	187	18	method	method	NOUN
ma-154	187	19	,	,	PUNCT
ma-154	187	20	j.	j.	PROPN
ma-154	187	21	complex	complex	PROPN
ma-154	187	22	.	.	PUNCT
ma-154	188	1	28	28	NUM
ma-154	188	2	(	(	PUNCT
ma-154	188	3	2012	2012	NUM
ma-154	188	4	)	)	PUNCT
ma-154	188	5	364	364	NUM
ma-154	188	6	-	-	SYM
ma-154	188	7	387	387	NUM
ma-154	188	8	.	.	PUNCT
ma-154	188	9	https://doi.org/10.1016/j.jco.2011.12.003.[5	https://doi.org/10.1016/j.jco.2011.12.003.[5	PROPN
ma-154	188	10	]	]	X
ma-154	188	11	i.k	i.k	PROPN
ma-154	188	12	.	.	PROPN
ma-154	188	13	argyros	argyros	PROPN
ma-154	188	14	,	,	PUNCT
ma-154	188	15	s.	s.	PROPN
ma-154	188	16	hilout	hilout	PROPN
ma-154	188	17	,	,	PUNCT
ma-154	188	18	on	on	ADP
ma-154	188	19	an	an	DET
ma-154	188	20	improved	improved	ADJ
ma-154	188	21	convergence	convergence	NOUN
ma-154	188	22	analysis	analysis	NOUN
ma-154	188	23	of	of	ADP
ma-154	188	24	newton	newton	PROPN
ma-154	188	25	’s	’s	PART
ma-154	188	26	method	method	NOUN
ma-154	188	27	,	,	PUNCT
ma-154	188	28	appl	appl	PROPN
ma-154	188	29	.	.	PROPN
ma-154	188	30	math	math	PROPN
ma-154	188	31	.	.	PUNCT
ma-154	189	1	comp	comp	PROPN
ma-154	189	2	.	.	PUNCT
ma-154	190	1	225	225	NUM
ma-154	190	2	(	(	PUNCT
ma-154	190	3	2013)372	2013)372	PROPN
ma-154	190	4	-	-	PUNCT
ma-154	190	5	386	386	NUM
ma-154	190	6	;	;	PUNCT
ma-154	190	7	https://doi.org/10.1016/j.amc.2013.09.049.[6	https://doi.org/10.1016/j.amc.2013.09.049.[6	CCONJ
ma-154	190	8	]	]	X
ma-154	190	9	i.k	i.k	PROPN
ma-154	190	10	.	.	PROPN
ma-154	190	11	argyros	argyros	PROPN
ma-154	190	12	,	,	PUNCT
ma-154	190	13	a.a	a.a	PROPN
ma-154	190	14	.	.	PROPN
ma-154	190	15	magréñan	magréñan	PROPN
ma-154	190	16	,	,	PUNCT
ma-154	190	17	a	a	DET
ma-154	190	18	contemporary	contemporary	ADJ
ma-154	190	19	study	study	NOUN
ma-154	190	20	of	of	ADP
ma-154	190	21	iterative	iterative	NOUN
ma-154	190	22	procedures	procedure	NOUN
ma-154	190	23	,	,	PUNCT
ma-154	190	24	elsevier	elsevier	NOUN
ma-154	190	25	(	(	PUNCT
ma-154	190	26	academic	academic	ADJ
ma-154	190	27	press	press	NOUN
ma-154	190	28	)	)	PUNCT
ma-154	190	29	,	,	PUNCT
ma-154	190	30	new	new	ADJ
ma-154	190	31	york,2018	york,2018	NOUN
ma-154	190	32	.	.	PUNCT
ma-154	191	1	https://doi.org/10.1016/c2015-0-04301-5.[7	https://doi.org/10.1016/c2015-0-04301-5.[7	PROPN
ma-154	191	2	]	]	X
ma-154	191	3	i.k	i.k	PROPN
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ma-154	193	4	)	)	PUNCT
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ma-154	193	6	-	-	SYM
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ma-154	193	8	.	.	PUNCT
ma-154	194	1	https://doi.org/10.1007/s13226-020-0409-5.[9	https://doi.org/10.1007/s13226-020-0409-5.[9	PRON
ma-154	194	2	]	]	X
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ma-154	195	1	appl	appl	PROPN
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ma-154	196	4	)	)	PUNCT
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ma-154	196	6	-	-	SYM
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ma-154	196	8	.	.	PUNCT
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ma-154	197	4	)	)	PUNCT
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ma-154	197	6	-	-	SYM
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ma-154	197	8	.	.	PUNCT
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ma-154	198	18	of	of	ADP
ma-154	198	19	kantorovich	kantorovich	PROPN
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ma-154	198	28	(	(	PUNCT
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ma-154	206	2	(	(	PUNCT
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ma-154	206	5	3	3	NUM
ma-154	206	6	-	-	SYM
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ma-154	206	8	.	.	PUNCT
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ma-154	208	5	.	.	PUNCT
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ma-154	209	2	/	/	SYM
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ma-154	212	2	.	.	PUNCT
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ma-154	213	2	/	/	SYM
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ma-154	213	4	/	/	SYM
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ma-154	215	1	https://	https://	PROPN
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