id	sid	tid	token	lemma	pos
ma-94	1	1	2022	2022	NUM
ma-94	1	2	ada	ada	PROPN
ma-94	1	3	academica	academica	PROPN
ma-94	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-94	1	5	.	.	PUNCT
ma-94	2	1	j.	j.	PROPN
ma-94	2	2	math	math	PROPN
ma-94	2	3	.	.	PUNCT
ma-94	3	1	anal	anal	ADJ
ma-94	3	2	.	.	PUNCT
ma-94	3	3	2	2	NUM
ma-94	3	4	(	(	PUNCT
ma-94	3	5	2022	2022	NUM
ma-94	3	6	)	)	PUNCT
ma-94	3	7	18doi	18doi	NUM
ma-94	3	8	:	:	PUNCT
ma-94	3	9	10.28924	10.28924	NUM
ma-94	3	10	/	/	SYM
ma-94	3	11	ada	ada	PROPN
ma-94	3	12	/	/	SYM
ma-94	3	13	ma.2.18	ma.2.18	PROPN
ma-94	3	14	developments	development	NOUN
ma-94	3	15	of	of	ADP
ma-94	3	16	newton	newton	PROPN
ma-94	3	17	’s	’s	PART
ma-94	3	18	method	method	NOUN
ma-94	3	19	under	under	ADP
ma-94	3	20	hölder	hölder	NOUN
ma-94	3	21	conditions	condition	NOUN
ma-94	3	22	samundra	samundra	VERB
ma-94	3	23	regmi1	regmi1	PROPN
ma-94	3	24	,	,	PUNCT
ma-94	3	25	ioannis	ioannis	PROPN
ma-94	3	26	k.	k.	PROPN
ma-94	3	27	argyros2,∗	argyros2,∗	PROPN
ma-94	3	28	,	,	PUNCT
ma-94	3	29	santhosh	santhosh	PROPN
ma-94	3	30	george3	george3	PROPN
ma-94	3	31	,	,	PUNCT
ma-94	3	32	christopher	christopher	PROPN
ma-94	3	33	i.	i.	PROPN
ma-94	4	1	argyros4	argyros4	PROPN
ma-94	5	1	1learning	1learning	NUM
ma-94	5	2	commons	common	NOUN
ma-94	5	3	,	,	PUNCT
ma-94	5	4	university	university	NOUN
ma-94	5	5	of	of	ADP
ma-94	5	6	north	north	PROPN
ma-94	5	7	texas	texas	PROPN
ma-94	5	8	at	at	ADP
ma-94	5	9	dallas	dallas	PROPN
ma-94	5	10	,	,	PUNCT
ma-94	5	11	dallas	dallas	PROPN
ma-94	5	12	,	,	PUNCT
ma-94	5	13	tx	tx	PROPN
ma-94	5	14	,	,	PUNCT
ma-94	5	15	usa	usa	PROPN
ma-94	5	16	samundra.regmi@untdallas.edu	samundra.regmi@untdallas.edu	PROPN
ma-94	5	17	2department	2department	PROPN
ma-94	5	18	of	of	ADP
ma-94	5	19	mathematical	mathematical	ADJ
ma-94	5	20	sciences	sciences	PROPN
ma-94	5	21	,	,	PUNCT
ma-94	5	22	cameron	cameron	PROPN
ma-94	5	23	university	university	PROPN
ma-94	5	24	,	,	PUNCT
ma-94	5	25	lawton	lawton	PROPN
ma-94	5	26	,	,	PUNCT
ma-94	5	27	ok	ok	PROPN
ma-94	5	28	73505	73505	NUM
ma-94	5	29	,	,	PUNCT
ma-94	5	30	usa	usa	PROPN
ma-94	5	31	iargyros@cameron.edu	iargyros@cameron.edu	PROPN
ma-94	6	1	3department	3department	NUM
ma-94	6	2	of	of	ADP
ma-94	6	3	mathematical	mathematical	ADJ
ma-94	6	4	and	and	CCONJ
ma-94	6	5	computational	computational	ADJ
ma-94	6	6	sciences	science	NOUN
ma-94	6	7	,	,	PUNCT
ma-94	6	8	national	national	PROPN
ma-94	6	9	institute	institute	PROPN
ma-94	6	10	of	of	ADP
ma-94	6	11	technology	technology	PROPN
ma-94	6	12	karnataka	karnataka	PROPN
ma-94	6	13	,	,	PUNCT
ma-94	6	14	india-575	india-575	ADJ
ma-94	6	15	025	025	NUM
ma-94	6	16	sgeorge@nitk.edu.in	sgeorge@nitk.edu.in	NOUN
ma-94	6	17	4department	4department	NUM
ma-94	6	18	of	of	ADP
ma-94	6	19	computing	computing	NOUN
ma-94	6	20	and	and	CCONJ
ma-94	6	21	technology	technology	NOUN
ma-94	6	22	,	,	PUNCT
ma-94	6	23	cameron	cameron	PROPN
ma-94	6	24	university	university	PROPN
ma-94	6	25	,	,	PUNCT
ma-94	6	26	lawton	lawton	PROPN
ma-94	6	27	,	,	PUNCT
ma-94	6	28	ok	ok	PROPN
ma-94	6	29	73505	73505	NUM
ma-94	6	30	,	,	PUNCT
ma-94	6	31	usa	usa	PROPN
ma-94	6	32	christopher.argyros@cameron.edu	christopher.argyros@cameron.edu	PROPN
ma-94	6	33	∗correspondence	∗correspondence	NOUN
ma-94	6	34	:	:	PUNCT
ma-94	6	35	iargyros@cameron.edu	iargyros@cameron.edu	X
ma-94	7	1	abstract	abstract	ADJ
ma-94	7	2	.	.	PUNCT
ma-94	8	1	the	the	DET
ma-94	8	2	semi	semi	ADJ
ma-94	8	3	-	-	ADJ
ma-94	8	4	local	local	ADJ
ma-94	8	5	convergence	convergence	NOUN
ma-94	8	6	criteria	criterion	NOUN
ma-94	8	7	for	for	ADP
ma-94	8	8	newton	newton	PROPN
ma-94	8	9	’s	’s	PART
ma-94	8	10	method	method	NOUN
ma-94	8	11	are	be	AUX
ma-94	8	12	weakened	weaken	VERB
ma-94	8	13	without	without	ADP
ma-94	8	14	new	new	ADJ
ma-94	8	15	con	con	NOUN
ma-94	8	16	-	-	PUNCT
ma-94	8	17	ditions	dition	NOUN
ma-94	8	18	.	.	PUNCT
ma-94	9	1	moreover	moreover	ADV
ma-94	9	2	,	,	PUNCT
ma-94	9	3	tighter	tight	ADJ
ma-94	9	4	error	error	NOUN
ma-94	9	5	distances	distance	NOUN
ma-94	9	6	are	be	AUX
ma-94	9	7	provided	provide	VERB
ma-94	9	8	as	as	ADV
ma-94	9	9	well	well	ADV
ma-94	9	10	as	as	ADP
ma-94	9	11	a	a	DET
ma-94	9	12	more	more	ADV
ma-94	9	13	precise	precise	ADJ
ma-94	9	14	information	information	NOUN
ma-94	9	15	on	on	ADP
ma-94	9	16	thelocation	thelocation	NOUN
ma-94	9	17	of	of	ADP
ma-94	9	18	the	the	DET
ma-94	9	19	solution	solution	NOUN
ma-94	9	20	.	.	PUNCT
ma-94	10	1	1	1	X
ma-94	10	2	.	.	X
ma-94	10	3	introduction	introduction	NOUN
ma-94	10	4	the	the	DET
ma-94	10	5	computation	computation	NOUN
ma-94	10	6	of	of	ADP
ma-94	10	7	a	a	DET
ma-94	10	8	solution	solution	NOUN
ma-94	10	9	x∗	x∗	PROPN
ma-94	10	10	of	of	ADP
ma-94	10	11	nonlinear	nonlinear	ADJ
ma-94	10	12	equation	equation	NOUN
ma-94	10	13	f	f	X
ma-94	10	14	(	(	PUNCT
ma-94	10	15	x	x	X
ma-94	10	16	)	)	PUNCT
ma-94	10	17	=	=	SYM
ma-94	10	18	0	0	PUNCT
ma-94	11	1	(	(	PUNCT
ma-94	11	2	1.1)is	1.1)is	NUM
ma-94	11	3	important	important	ADJ
ma-94	11	4	in	in	ADP
ma-94	11	5	computational	computational	ADJ
ma-94	11	6	sciences	science	NOUN
ma-94	11	7	,	,	PUNCT
ma-94	11	8	since	since	SCONJ
ma-94	11	9	many	many	ADJ
ma-94	11	10	applications	application	NOUN
ma-94	11	11	can	can	AUX
ma-94	11	12	be	be	AUX
ma-94	11	13	written	write	VERB
ma-94	11	14	as	as	ADP
ma-94	11	15	(	(	PUNCT
ma-94	11	16	1.1	1.1	NUM
ma-94	11	17	)	)	PUNCT
ma-94	11	18	.	.	PUNCT
ma-94	12	1	here	here	ADV
ma-94	12	2	f	f	X
ma-94	12	3	:	:	PUNCT
ma-94	12	4	ω	ω	NUM
ma-94	12	5	⊆	⊆	NUM
ma-94	12	6	x	x	SYM
ma-94	12	7	−→	−→	NOUN
ma-94	12	8	y	y	PROPN
ma-94	12	9	is	be	AUX
ma-94	12	10	fréchet	fréchet	NOUN
ma-94	12	11	-	-	PUNCT
ma-94	12	12	differentiable	differentiable	ADJ
ma-94	12	13	operator	operator	NOUN
ma-94	12	14	,	,	PUNCT
ma-94	12	15	x	x	PRON
ma-94	12	16	,	,	PUNCT
ma-94	12	17	y	y	PROPN
ma-94	12	18	are	be	AUX
ma-94	12	19	banach	banach	NOUN
ma-94	12	20	spaces	space	NOUN
ma-94	12	21	and	and	CCONJ
ma-94	12	22	ω	ω	NUM
ma-94	12	23	6=	6=	NOUN
ma-94	12	24	∅	∅	NOUN
ma-94	12	25	is	be	AUX
ma-94	12	26	aconvex	aconvex	ADJ
ma-94	12	27	and	and	CCONJ
ma-94	12	28	open	open	ADJ
ma-94	12	29	set	set	NOUN
ma-94	12	30	.	.	PUNCT
ma-94	13	1	but	but	CCONJ
ma-94	13	2	this	this	PRON
ma-94	13	3	can	can	AUX
ma-94	13	4	be	be	AUX
ma-94	13	5	attained	attain	VERB
ma-94	13	6	only	only	ADV
ma-94	13	7	in	in	ADP
ma-94	13	8	special	special	ADJ
ma-94	13	9	cases	case	NOUN
ma-94	13	10	.	.	PUNCT
ma-94	14	1	that	that	PRON
ma-94	14	2	explains	explain	VERB
ma-94	14	3	why	why	SCONJ
ma-94	14	4	mostsolution	mostsolution	NOUN
ma-94	14	5	methods	method	NOUN
ma-94	14	6	for	for	ADP
ma-94	14	7	(	(	PUNCT
ma-94	14	8	1.1	1.1	NUM
ma-94	14	9	)	)	PUNCT
ma-94	14	10	are	be	AUX
ma-94	14	11	iterative	iterative	NOUN
ma-94	14	12	.	.	PUNCT
ma-94	15	1	there	there	PRON
ma-94	15	2	is	be	VERB
ma-94	15	3	a	a	DET
ma-94	15	4	plethora	plethora	NOUN
ma-94	15	5	of	of	ADP
ma-94	15	6	methods	method	NOUN
ma-94	15	7	for	for	ADP
ma-94	15	8	solving	solve	VERB
ma-94	15	9	(	(	PUNCT
ma-94	15	10	1.1	1.1	NUM
ma-94	15	11	)	)	PUNCT
ma-94	16	1	[	[	X
ma-94	16	2	1–14].among	1–14].among	NUM
ma-94	16	3	them	they	PRON
ma-94	16	4	newton	newton	PROPN
ma-94	16	5	’s	’s	PART
ma-94	16	6	method	method	NOUN
ma-94	16	7	(	(	PUNCT
ma-94	16	8	nm	nm	NOUN
ma-94	16	9	)	)	PUNCT
ma-94	16	10	defined	define	VERB
ma-94	16	11	by	by	ADP
ma-94	16	12	x0	x0	PROPN
ma-94	16	13	∈	∈	PROPN
ma-94	16	14	ω	ω	PROPN
ma-94	16	15	,	,	PUNCT
ma-94	16	16	xn+1	xn+1	PROPN
ma-94	16	17	=	=	SYM
ma-94	16	18	xn	xn	PROPN
ma-94	17	1	−	−	PROPN
ma-94	17	2	f	f	PROPN
ma-94	17	3	′(xn)−1f	′(xn)−1f	PROPN
ma-94	17	4	(	(	PUNCT
ma-94	17	5	xn	xn	PROPN
ma-94	17	6	)	)	PUNCT
ma-94	17	7	(	(	PUNCT
ma-94	17	8	1.2	1.2	NUM
ma-94	17	9	)	)	PUNCT
ma-94	17	10	seems	seem	VERB
ma-94	17	11	to	to	PART
ma-94	17	12	be	be	AUX
ma-94	17	13	the	the	DET
ma-94	17	14	most	most	ADV
ma-94	17	15	popular	popular	ADJ
ma-94	18	1	[	[	X
ma-94	18	2	2,4	2,4	NUM
ma-94	18	3	]	]	X
ma-94	18	4	.	.	PUNCT
ma-94	19	1	but	but	CCONJ
ma-94	19	2	the	the	DET
ma-94	19	3	convergence	convergence	NOUN
ma-94	19	4	domain	domain	NOUN
ma-94	19	5	is	be	AUX
ma-94	19	6	small	small	ADJ
ma-94	19	7	,	,	PUNCT
ma-94	19	8	limiting	limit	VERB
ma-94	19	9	the	the	DET
ma-94	19	10	applicability	applicability	NOUN
ma-94	19	11	ofnm	ofnm	NOUN
ma-94	19	12	.	.	PUNCT
ma-94	20	1	that	that	PRON
ma-94	20	2	is	be	AUX
ma-94	20	3	why	why	SCONJ
ma-94	20	4	we	we	PRON
ma-94	20	5	have	have	AUX
ma-94	20	6	developed	develop	VERB
ma-94	20	7	a	a	DET
ma-94	20	8	technique	technique	NOUN
ma-94	20	9	that	that	PRON
ma-94	20	10	determines	determine	VERB
ma-94	20	11	a	a	DET
ma-94	20	12	subset	subset	NOUN
ma-94	20	13	ω0	ω0	NOUN
ma-94	20	14	of	of	ADP
ma-94	20	15	ω	ω	PROPN
ma-94	20	16	also	also	ADV
ma-94	20	17	containingthe	containingthe	PROPN
ma-94	20	18	iterates	iterate	NOUN
ma-94	20	19	{	{	PUNCT
ma-94	20	20	xn	xn	NUM
ma-94	20	21	}	}	PUNCT
ma-94	20	22	.	.	PUNCT
ma-94	21	1	hence	hence	ADV
ma-94	21	2	,	,	PUNCT
ma-94	21	3	the	the	DET
ma-94	21	4	hölder	hölder	NOUN
ma-94	21	5	constants	constant	NOUN
ma-94	21	6	are	be	AUX
ma-94	21	7	at	at	ADV
ma-94	21	8	least	least	ADJ
ma-94	21	9	as	as	ADV
ma-94	21	10	tight	tight	ADJ
ma-94	21	11	as	as	ADP
ma-94	21	12	the	the	DET
ma-94	21	13	ones	one	NOUN
ma-94	21	14	in	in	ADP
ma-94	21	15	ω	ω	PROPN
ma-94	21	16	.	.	PUNCT
ma-94	22	1	this	this	DET
ma-94	22	2	crucial	crucial	ADJ
ma-94	22	3	received	receive	VERB
ma-94	22	4	:	:	PUNCT
ma-94	22	5	20	20	NUM
ma-94	22	6	mar	mar	PROPN
ma-94	22	7	2022	2022	NUM
ma-94	22	8	.	.	PUNCT
ma-94	23	1	key	key	ADJ
ma-94	23	2	words	word	NOUN
ma-94	23	3	and	and	CCONJ
ma-94	23	4	phrases	phrase	NOUN
ma-94	23	5	.	.	PUNCT
ma-94	24	1	banach	banach	NOUN
ma-94	24	2	space	space	NOUN
ma-94	24	3	;	;	PUNCT
ma-94	24	4	hölder	hölder	NOUN
ma-94	24	5	condition	condition	NOUN
ma-94	24	6	;	;	PUNCT
ma-94	24	7	semi	semi	ADJ
ma-94	24	8	-	-	ADJ
ma-94	24	9	local	local	ADJ
ma-94	24	10	convergence	convergence	NOUN
ma-94	24	11	;	;	PUNCT
ma-94	24	12	convergence	convergence	NOUN
ma-94	24	13	criteria.1	criteria.1	NOUN
ma-94	24	14	https://adac.ee	https://adac.ee	PROPN
ma-94	24	15	https://doi.org/10.28924/ada/ma.2.18	https://doi.org/10.28924/ada/ma.2.18	PROPN
ma-94	24	16	eur	eur	PROPN
ma-94	24	17	.	.	PUNCT
ma-94	25	1	j.	j.	PROPN
ma-94	25	2	math	math	PROPN
ma-94	25	3	.	.	PUNCT
ma-94	26	1	anal	anal	PROPN
ma-94	26	2	.	.	PUNCT
ma-94	27	1	10.28924	10.28924	NUM
ma-94	27	2	/	/	SYM
ma-94	27	3	ada	ada	PROPN
ma-94	27	4	/	/	SYM
ma-94	27	5	ma.2.18	ma.2.18	PROPN
ma-94	27	6	2modification	2modification	PROPN
ma-94	27	7	leads	lead	VERB
ma-94	27	8	to	to	ADP
ma-94	27	9	:	:	PUNCT
ma-94	27	10	weaker	weak	ADJ
ma-94	27	11	sufficient	sufficient	ADJ
ma-94	27	12	convergence	convergence	NOUN
ma-94	27	13	criteria	criterion	NOUN
ma-94	27	14	,	,	PUNCT
ma-94	27	15	the	the	DET
ma-94	27	16	extension	extension	NOUN
ma-94	27	17	of	of	ADP
ma-94	27	18	the	the	DET
ma-94	27	19	convergencedomain	convergencedomain	NOUN
ma-94	27	20	,	,	PUNCT
ma-94	27	21	tighter	tight	ADJ
ma-94	27	22	error	error	NOUN
ma-94	27	23	estimates	estimate	NOUN
ma-94	27	24	on	on	ADP
ma-94	27	25	‖x∗	‖x∗	PUNCT
ma-94	27	26	−	−	PROPN
ma-94	27	27	xn‖	xn‖	PROPN
ma-94	27	28	,	,	PUNCT
ma-94	27	29	‖xn+1	‖xn+1	NUM
ma-94	27	30	−	−	NOUN
ma-94	27	31	xn‖	xn‖	PROPN
ma-94	27	32	and	and	CCONJ
ma-94	27	33	a	a	DET
ma-94	27	34	more	more	ADV
ma-94	27	35	precise	precise	ADJ
ma-94	27	36	information	information	NOUN
ma-94	27	37	on	on	ADP
ma-94	27	38	x∗.it	x∗.it	PROPN
ma-94	27	39	is	be	AUX
ma-94	27	40	worth	worth	ADJ
ma-94	27	41	noticing	notice	VERB
ma-94	27	42	that	that	SCONJ
ma-94	27	43	these	these	DET
ma-94	27	44	advantages	advantage	NOUN
ma-94	27	45	are	be	AUX
ma-94	27	46	obtained	obtain	VERB
ma-94	27	47	without	without	ADP
ma-94	27	48	additional	additional	ADJ
ma-94	27	49	conditions	condition	NOUN
ma-94	27	50	,	,	PUNCT
ma-94	27	51	since	since	SCONJ
ma-94	27	52	inpractice	inpractice	VERB
ma-94	27	53	the	the	DET
ma-94	27	54	evolution	evolution	NOUN
ma-94	27	55	of	of	ADP
ma-94	27	56	the	the	DET
ma-94	27	57	old	old	ADJ
ma-94	27	58	hölderian	hölderian	ADJ
ma-94	27	59	constants	constant	NOUN
ma-94	27	60	require	require	VERB
ma-94	27	61	that	that	SCONJ
ma-94	27	62	of	of	ADP
ma-94	27	63	the	the	DET
ma-94	27	64	new	new	ADJ
ma-94	27	65	conditions	condition	NOUN
ma-94	27	66	as	as	ADP
ma-94	27	67	specialcases	specialcase	NOUN
ma-94	27	68	.	.	PUNCT
ma-94	28	1	2	2	X
ma-94	28	2	.	.	X
ma-94	28	3	convergence	convergence	NOUN
ma-94	28	4	we	we	PRON
ma-94	28	5	introduce	introduce	VERB
ma-94	28	6	certain	certain	ADJ
ma-94	28	7	hölder	hölder	NOUN
ma-94	28	8	conditions	condition	NOUN
ma-94	28	9	crucial	crucial	ADJ
ma-94	28	10	for	for	ADP
ma-94	28	11	the	the	DET
ma-94	28	12	semi	semi	ADJ
ma-94	28	13	-	-	ADJ
ma-94	28	14	local	local	ADJ
ma-94	28	15	convergence	convergence	NOUN
ma-94	28	16	.	.	PUNCT
ma-94	29	1	let	let	VERB
ma-94	29	2	p	p	X
ma-94	29	3	∈	∈	PROPN
ma-94	29	4	(	(	PUNCT
ma-94	29	5	0	0	NUM
ma-94	29	6	,	,	PUNCT
ma-94	29	7	1].suppose	1].suppose	NUM
ma-94	29	8	there	there	PRON
ma-94	29	9	exists	exist	VERB
ma-94	29	10	x0	x0	PROPN
ma-94	29	11	∈	∈	PROPN
ma-94	29	12	ω	ω	NUM
ma-94	29	13	such	such	ADJ
ma-94	29	14	that	that	SCONJ
ma-94	29	15	f	f	PROPN
ma-94	29	16	′(x0)−1	′(x0)−1	PROPN
ma-94	29	17	∈	∈	PROPN
ma-94	29	18	l(y	l(y	PROPN
ma-94	29	19	,	,	PUNCT
ma-94	29	20	x	x	NOUN
ma-94	29	21	)	)	PUNCT
ma-94	29	22	.	.	PUNCT
ma-94	30	1	definition	definition	NOUN
ma-94	30	2	2.1	2.1	NUM
ma-94	30	3	.	.	PUNCT
ma-94	31	1	operator	operator	NOUN
ma-94	31	2	f	f	PROPN
ma-94	31	3	′	′	NOUN
ma-94	31	4	is	be	AUX
ma-94	31	5	center	center	ADJ
ma-94	31	6	hölderian	hölderian	ADJ
ma-94	31	7	on	on	ADP
ma-94	31	8	ω	ω	NUM
ma-94	31	9	if	if	SCONJ
ma-94	31	10	there	there	PRON
ma-94	31	11	exists	exist	VERB
ma-94	31	12	h0	h0	PROPN
ma-94	31	13	>	>	X
ma-94	31	14	0	0	NUM
ma-94	32	1	such	such	ADJ
ma-94	32	2	that	that	SCONJ
ma-94	32	3	‖f	‖f	PRON
ma-94	32	4	′(x0)−1f	′(x0)−1f	NOUN
ma-94	32	5	′(w)−	′(w)−	VERB
ma-94	32	6	f	f	PROPN
ma-94	32	7	′(x0)‖	′(x0)‖	NOUN
ma-94	32	8	≤	≤	ADJ
ma-94	32	9	h0‖w	h0‖w	NOUN
ma-94	33	1	−	−	NOUN
ma-94	33	2	x0‖p	x0‖p	NUM
ma-94	33	3	(	(	PUNCT
ma-94	33	4	2.1	2.1	NUM
ma-94	33	5	)	)	PUNCT
ma-94	33	6	for	for	ADP
ma-94	33	7	all	all	DET
ma-94	33	8	w	w	PROPN
ma-94	33	9	∈	∈	PROPN
ma-94	33	10	ω	ω	PROPN
ma-94	33	11	.	.	PUNCT
ma-94	34	1	set	set	VERB
ma-94	34	2	ω0	ω0	NOUN
ma-94	34	3	=	=	SYM
ma-94	34	4	u(x0	u(x0	NOUN
ma-94	34	5	,	,	PUNCT
ma-94	34	6	1	1	NUM
ma-94	34	7	h	h	NOUN
ma-94	34	8	1	1	NUM
ma-94	34	9	p	p	NOUN
ma-94	34	10	0	0	NUM
ma-94	34	11	)	)	PUNCT
ma-94	35	1	∩ω	∩ω	INTJ
ma-94	35	2	.	.	PUNCT
ma-94	36	1	(	(	PUNCT
ma-94	36	2	2.2	2.2	NUM
ma-94	36	3	)	)	PUNCT
ma-94	36	4	definition	definition	NOUN
ma-94	36	5	2.2	2.2	NUM
ma-94	36	6	.	.	PUNCT
ma-94	37	1	operator	operator	NOUN
ma-94	37	2	f	f	PROPN
ma-94	37	3	′	′	NOUN
ma-94	37	4	is	be	AUX
ma-94	37	5	center	center	ADJ
ma-94	37	6	hölderian	hölderian	ADJ
ma-94	37	7	on	on	ADP
ma-94	37	8	ω0	ω0	NOUN
ma-94	37	9	if	if	SCONJ
ma-94	37	10	there	there	PRON
ma-94	37	11	exists	exist	VERB
ma-94	37	12	h	h	NOUN
ma-94	37	13	>	>	X
ma-94	37	14	0	0	NUM
ma-94	37	15	such	such	ADJ
ma-94	37	16	that	that	SCONJ
ma-94	37	17	‖f	‖f	PRON
ma-94	37	18	′(x0)−1f	′(x0)−1f	NOUN
ma-94	37	19	′(w)−	′(w)−	VERB
ma-94	37	20	f	f	PROPN
ma-94	37	21	′(u)‖	′(u)‖	PROPN
ma-94	37	22	≤	≤	PROPN
ma-94	37	23	h̃‖w	h̃‖w	VERB
ma-94	37	24	−	−	PROPN
ma-94	37	25	u‖p	u‖p	NOUN
ma-94	37	26	,	,	PUNCT
ma-94	37	27	(	(	PUNCT
ma-94	37	28	2.3	2.3	NUM
ma-94	37	29	)	)	PUNCT
ma-94	37	30	where	where	SCONJ
ma-94	37	31	h̃	h̃	PROPN
ma-94	37	32	=	=	SYM
ma-94	37	33	{	{	PUNCT
ma-94	37	34	h	h	NOUN
ma-94	37	35	,	,	PUNCT
ma-94	37	36	w	w	PROPN
ma-94	37	37	=	=	SYM
ma-94	37	38	u	u	NOUN
ma-94	37	39	−	−	PROPN
ma-94	37	40	f	f	NOUN
ma-94	37	41	′(u)−1f	′(u)−1f	NOUN
ma-94	37	42	(	(	PUNCT
ma-94	37	43	u	u	NOUN
ma-94	37	44	)	)	PUNCT
ma-94	37	45	,	,	PUNCT
ma-94	37	46	u	u	PROPN
ma-94	37	47	∈	∈	NOUN
ma-94	37	48	d0	d0	PROPN
ma-94	37	49	k	k	PROPN
ma-94	37	50	,	,	PUNCT
ma-94	37	51	w	w	PROPN
ma-94	37	52	,	,	PUNCT
ma-94	37	53	u	u	PROPN
ma-94	37	54	∈	∈	PROPN
ma-94	37	55	ω0	ω0	NOUN
ma-94	37	56	.	.	PUNCT
ma-94	37	57	.	.	PUNCT
ma-94	38	1	we	we	PRON
ma-94	38	2	present	present	VERB
ma-94	38	3	the	the	DET
ma-94	38	4	results	result	NOUN
ma-94	38	5	with	with	ADP
ma-94	38	6	h	h	NOUN
ma-94	38	7	although	although	SCONJ
ma-94	38	8	k	k	PROPN
ma-94	38	9	can	can	AUX
ma-94	38	10	be	be	AUX
ma-94	38	11	used	use	VERB
ma-94	38	12	too	too	ADV
ma-94	38	13	.	.	PUNCT
ma-94	39	1	but	but	CCONJ
ma-94	39	2	notice	notice	VERB
ma-94	39	3	h	h	NOUN
ma-94	39	4	≤	≤	PROPN
ma-94	39	5	k.	k.	PROPN
ma-94	39	6	definition	definition	NOUN
ma-94	39	7	2.3	2.3	NUM
ma-94	39	8	.	.	PUNCT
ma-94	40	1	operator	operator	NOUN
ma-94	40	2	f	f	PROPN
ma-94	40	3	′	′	NOUN
ma-94	40	4	is	be	AUX
ma-94	40	5	center	center	ADJ
ma-94	40	6	hölderian	hölderian	ADJ
ma-94	40	7	on	on	ADP
ma-94	40	8	ω	ω	NUM
ma-94	40	9	if	if	SCONJ
ma-94	40	10	there	there	PRON
ma-94	40	11	exists	exist	VERB
ma-94	40	12	h1	h1	PROPN
ma-94	40	13	>	>	X
ma-94	40	14	0	0	NUM
ma-94	40	15	such	such	ADJ
ma-94	40	16	that	that	SCONJ
ma-94	40	17	‖f	‖f	PRON
ma-94	40	18	′(x0)−1f	′(x0)−1f	NOUN
ma-94	40	19	′(w)−	′(w)−	VERB
ma-94	40	20	f	f	PROPN
ma-94	40	21	′(u)‖	′(u)‖	PROPN
ma-94	40	22	≤	≤	PROPN
ma-94	40	23	h1‖w	h1‖w	NOUN
ma-94	40	24	−	−	NOUN
ma-94	40	25	u‖p	u‖p	NOUN
ma-94	40	26	(	(	PUNCT
ma-94	40	27	2.4	2.4	NUM
ma-94	40	28	)	)	PUNCT
ma-94	40	29	for	for	ADP
ma-94	40	30	all	all	DET
ma-94	40	31	w	w	NOUN
ma-94	40	32	,	,	PUNCT
ma-94	40	33	u	u	PROPN
ma-94	40	34	∈	∈	PROPN
ma-94	40	35	ω	ω	PROPN
ma-94	40	36	.	.	PUNCT
ma-94	40	37	remark	remark	PROPN
ma-94	40	38	2.4	2.4	NUM
ma-94	40	39	.	.	PUNCT
ma-94	41	1	it	it	PRON
ma-94	41	2	follows	follow	VERB
ma-94	41	3	from	from	ADP
ma-94	41	4	(	(	PUNCT
ma-94	41	5	2.2	2.2	NUM
ma-94	41	6	)	)	PUNCT
ma-94	41	7	,	,	PUNCT
ma-94	41	8	that	that	PRON
ma-94	41	9	ω0	ω0	VERB
ma-94	41	10	⊆	⊆	NUM
ma-94	41	11	ω	ω	NOUN
ma-94	41	12	.	.	PUNCT
ma-94	42	1	(	(	PUNCT
ma-94	42	2	2.5	2.5	NUM
ma-94	42	3	)	)	PUNCT
ma-94	42	4	then	then	ADV
ma-94	42	5	,	,	PUNCT
ma-94	42	6	by	by	ADP
ma-94	42	7	(	(	PUNCT
ma-94	42	8	2.1)-(2.5	2.1)-(2.5	NOUN
ma-94	42	9	)	)	PUNCT
ma-94	42	10	the	the	DET
ma-94	42	11	following	follow	VERB
ma-94	42	12	items	item	NOUN
ma-94	42	13	hold	hold	VERB
ma-94	42	14	h0	h0	NOUN
ma-94	42	15	≤	≤	PROPN
ma-94	42	16	h1	h1	NOUN
ma-94	42	17	(	(	PUNCT
ma-94	42	18	2.6	2.6	NUM
ma-94	42	19	)	)	PUNCT
ma-94	42	20	and	and	CCONJ
ma-94	42	21	h	h	PROPN
ma-94	42	22	≤	≤	X
ma-94	42	23	h1	h1	PROPN
ma-94	42	24	.	.	PUNCT
ma-94	43	1	(	(	PUNCT
ma-94	43	2	2.7	2.7	NUM
ma-94	43	3	)	)	PUNCT
ma-94	43	4	we	we	PRON
ma-94	43	5	shall	shall	AUX
ma-94	43	6	assume	assume	VERB
ma-94	43	7	that	that	SCONJ
ma-94	43	8	h0	h0	PROPN
ma-94	43	9	≤	≤	PROPN
ma-94	43	10	h.	h.	NOUN
ma-94	43	11	(	(	PUNCT
ma-94	43	12	2.8	2.8	NUM
ma-94	43	13	)	)	PUNCT
ma-94	43	14	https://doi.org/10.28924/ada/ma.2.18	https://doi.org/10.28924/ada/ma.2.18	PROPN
ma-94	43	15	eur	eur	PROPN
ma-94	43	16	.	.	PUNCT
ma-94	44	1	j.	j.	PROPN
ma-94	44	2	math	math	PROPN
ma-94	44	3	.	.	PUNCT
ma-94	45	1	anal	anal	PROPN
ma-94	45	2	.	.	PUNCT
ma-94	46	1	10.28924	10.28924	NUM
ma-94	46	2	/	/	SYM
ma-94	46	3	ada	ada	PROPN
ma-94	46	4	/	/	SYM
ma-94	46	5	ma.2.18	ma.2.18	PROPN
ma-94	46	6	3	3	NUM
ma-94	46	7	otherwise	otherwise	ADV
ma-94	46	8	the	the	DET
ma-94	46	9	results	result	NOUN
ma-94	46	10	that	that	PRON
ma-94	46	11	follow	follow	VERB
ma-94	46	12	hold	hold	NOUN
ma-94	46	13	with	with	ADP
ma-94	46	14	h0	h0	NOUN
ma-94	46	15	replacing	replace	VERB
ma-94	46	16	h.	h.	NOUN
ma-94	46	17	notice	notice	VERB
ma-94	46	18	that	that	SCONJ
ma-94	46	19	h0	h0	NOUN
ma-94	46	20	=	=	SYM
ma-94	46	21	h0(x0,ω	h0(x0,ω	ADJ
ma-94	46	22	)	)	PUNCT
ma-94	46	23	,	,	PUNCT
ma-94	46	24	h1	h1	PROPN
ma-94	46	25	=	=	PUNCT
ma-94	46	26	h1(x0,ω	h1(x0,ω	X
ma-94	46	27	)	)	PUNCT
ma-94	46	28	,	,	PUNCT
ma-94	46	29	h	h	NOUN
ma-94	46	30	=	=	SYM
ma-94	46	31	h(x0,ω0	h(x0,ω0	PROPN
ma-94	46	32	)	)	PUNCT
ma-94	46	33	and	and	CCONJ
ma-94	46	34	h0	h0	PROPN
ma-94	46	35	h1	h1	PROPN
ma-94	46	36	can	can	AUX
ma-94	46	37	be	be	AUX
ma-94	46	38	small	small	ADJ
ma-94	46	39	(	(	PUNCT
ma-94	46	40	arbitrarily	arbitrarily	ADV
ma-94	46	41	)	)	PUNCT
ma-94	47	1	[	[	X
ma-94	47	2	2–4	2–4	NUM
ma-94	47	3	]	]	X
ma-94	47	4	.	.	PUNCT
ma-94	48	1	in	in	ADP
ma-94	48	2	earlier	early	ADJ
ma-94	48	3	studies	study	NOUN
ma-94	48	4	[	[	X
ma-94	48	5	1	1	NUM
ma-94	48	6	,	,	PUNCT
ma-94	48	7	5–14	5–14	PROPN
ma-94	48	8	]	]	X
ma-94	48	9	the	the	DET
ma-94	48	10	estimate	estimate	NOUN
ma-94	48	11	‖f	‖f	ADP
ma-94	48	12	′(z)−1f	′(z)−1f	NOUN
ma-94	48	13	′(x0)‖	′(x0)‖	X
ma-94	48	14	≤	≤	NOUN
ma-94	48	15	1	1	NUM
ma-94	48	16	1−h1‖z	1−h1‖z	NUM
ma-94	48	17	−	−	NOUN
ma-94	48	18	x0‖	x0‖	PROPN
ma-94	48	19	1	1	NUM
ma-94	48	20	p	p	NOUN
ma-94	48	21	(	(	PUNCT
ma-94	48	22	2.9	2.9	NUM
ma-94	48	23	)	)	PUNCT
ma-94	48	24	for	for	ADP
ma-94	48	25	all	all	DET
ma-94	48	26	z	z	NOUN
ma-94	48	27	∈	∈	PROPN
ma-94	48	28	u(x0	u(x0	NOUN
ma-94	48	29	,	,	PUNCT
ma-94	48	30	1	1	NUM
ma-94	48	31	h	h	NOUN
ma-94	48	32	1	1	NUM
ma-94	48	33	p	p	NOUN
ma-94	48	34	1	1	NUM
ma-94	48	35	)	)	PUNCT
ma-94	48	36	was	be	AUX
ma-94	48	37	found	find	VERB
ma-94	48	38	using	use	VERB
ma-94	48	39	(	(	PUNCT
ma-94	48	40	2.4	2.4	NUM
ma-94	48	41	)	)	PUNCT
ma-94	48	42	.	.	PUNCT
ma-94	49	1	but	but	CCONJ
ma-94	49	2	,	,	PUNCT
ma-94	49	3	if	if	SCONJ
ma-94	49	4	we	we	PRON
ma-94	49	5	use	use	VERB
ma-94	49	6	(	(	PUNCT
ma-94	49	7	2.1	2.1	NUM
ma-94	49	8	)	)	PUNCT
ma-94	49	9	to	to	PART
ma-94	49	10	obtain	obtain	VERB
ma-94	49	11	the	the	DET
ma-94	49	12	weaker	weak	ADJ
ma-94	49	13	and	and	CCONJ
ma-94	49	14	more	more	ADV
ma-94	49	15	precise	precise	ADJ
ma-94	49	16	estimate	estimate	NOUN
ma-94	49	17	‖f	‖f	ADP
ma-94	49	18	′(z)−1f	′(z)−1f	NOUN
ma-94	49	19	′(x0)‖	′(x0)‖	X
ma-94	49	20	≤	≤	ADV
ma-94	49	21	1	1	NUM
ma-94	49	22	1−h0‖z	1−h0‖z	NUM
ma-94	49	23	−	−	PROPN
ma-94	49	24	x0‖	x0‖	PROPN
ma-94	49	25	1	1	NUM
ma-94	49	26	p	p	NOUN
ma-94	49	27	(	(	PUNCT
ma-94	49	28	2.10	2.10	NUM
ma-94	49	29	)	)	PUNCT
ma-94	49	30	for	for	ADP
ma-94	49	31	all	all	DET
ma-94	49	32	z	z	NOUN
ma-94	49	33	∈	∈	PROPN
ma-94	49	34	u(x0	u(x0	NOUN
ma-94	49	35	,	,	PUNCT
ma-94	49	36	1	1	NUM
ma-94	49	37	h	h	NOUN
ma-94	49	38	1	1	NUM
ma-94	49	39	p	p	NOUN
ma-94	49	40	0	0	NUM
ma-94	49	41	)	)	PUNCT
ma-94	49	42	.	.	PUNCT
ma-94	50	1	this	this	DET
ma-94	50	2	modification	modification	NOUN
ma-94	50	3	in	in	ADP
ma-94	50	4	the	the	DET
ma-94	50	5	proofs	proof	NOUN
ma-94	50	6	and	and	CCONJ
ma-94	50	7	exchanging	exchange	VERB
ma-94	50	8	h1	h1	NOUN
ma-94	50	9	by	by	ADP
ma-94	50	10	h	h	NOUN
ma-94	50	11	leads	lead	VERB
ma-94	50	12	to	to	ADP
ma-94	50	13	the	the	DET
ma-94	50	14	advantages	advantage	NOUN
ma-94	50	15	as	as	SCONJ
ma-94	50	16	already	already	ADV
ma-94	50	17	mentioned	mention	VERB
ma-94	50	18	in	in	ADP
ma-94	50	19	the	the	DET
ma-94	50	20	introduction	introduction	NOUN
ma-94	50	21	.	.	PUNCT
ma-94	51	1	that	that	PRON
ma-94	51	2	is	be	AUX
ma-94	51	3	why	why	SCONJ
ma-94	51	4	we	we	PRON
ma-94	51	5	omit	omit	VERB
ma-94	51	6	the	the	DET
ma-94	51	7	proofs	proof	NOUN
ma-94	51	8	in	in	ADP
ma-94	51	9	our	our	PRON
ma-94	51	10	results	result	NOUN
ma-94	51	11	that	that	PRON
ma-94	51	12	follow	follow	VERB
ma-94	51	13	.	.	PUNCT
ma-94	52	1	notice	notice	NOUN
ma-94	52	2	also	also	ADV
ma-94	52	3	that	that	SCONJ
ma-94	52	4	in	in	ADP
ma-94	52	5	practice	practice	NOUN
ma-94	52	6	the	the	DET
ma-94	52	7	computation	computation	NOUN
ma-94	52	8	of	of	ADP
ma-94	52	9	h1	h1	PROPN
ma-94	52	10	require	require	VERB
ma-94	52	11	that	that	PRON
ma-94	52	12	of	of	ADP
ma-94	52	13	h0	h0	PROPN
ma-94	52	14	and	and	CCONJ
ma-94	52	15	h	h	NOUN
ma-94	52	16	as	as	ADP
ma-94	52	17	special	special	ADJ
ma-94	52	18	cases	case	NOUN
ma-94	52	19	.	.	PUNCT
ma-94	53	1	hence	hence	ADV
ma-94	53	2	,	,	PUNCT
ma-94	53	3	the	the	DET
ma-94	53	4	applicability	applicability	NOUN
ma-94	53	5	of	of	ADP
ma-94	53	6	nm	nm	NOUN
ma-94	53	7	is	be	AUX
ma-94	53	8	extended	extend	VERB
ma-94	53	9	without	without	ADP
ma-94	53	10	additional	additional	ADJ
ma-94	53	11	conditions	condition	NOUN
ma-94	53	12	.	.	PUNCT
ma-94	54	1	let	let	VERB
ma-94	54	2	d	d	X
ma-94	54	3	≥	≥	X
ma-94	54	4	0	0	NUM
ma-94	54	5	be	be	AUX
ma-94	54	6	such	such	ADJ
ma-94	54	7	that	that	SCONJ
ma-94	54	8	‖f	‖f	ADJ
ma-94	54	9	′(x0)−1f	′(x0)−1f	NOUN
ma-94	54	10	(	(	PUNCT
ma-94	54	11	x0)‖	x0)‖	PROPN
ma-94	54	12	≤	≤	PROPN
ma-94	54	13	d.	d.	NOUN
ma-94	54	14	(	(	PUNCT
ma-94	54	15	2.11	2.11	NUM
ma-94	54	16	)	)	PUNCT
ma-94	54	17	we	we	PRON
ma-94	54	18	assume	assume	VERB
ma-94	54	19	that	that	SCONJ
ma-94	54	20	(	(	PUNCT
ma-94	54	21	2.1)-(2.3	2.1)-(2.3	NUM
ma-94	54	22	)	)	PUNCT
ma-94	54	23	hold	hold	NOUN
ma-94	54	24	from	from	ADP
ma-94	54	25	now	now	ADV
ma-94	54	26	on	on	ADV
ma-94	54	27	unless	unless	SCONJ
ma-94	54	28	otherwise	otherwise	ADV
ma-94	54	29	stated	state	VERB
ma-94	54	30	.	.	PUNCT
ma-94	55	1	first	first	ADV
ma-94	55	2	we	we	PRON
ma-94	55	3	extend	extend	VERB
ma-94	55	4	the	the	DET
ma-94	55	5	resultsby	resultsby	ADJ
ma-94	55	6	keller	keller	NOUN
ma-94	55	7	[	[	X
ma-94	55	8	11	11	NUM
ma-94	55	9	]	]	PUNCT
ma-94	55	10	for	for	ADP
ma-94	55	11	nm	nm	NOUN
ma-94	55	12	.	.	PUNCT
ma-94	56	1	similarly	similarly	ADV
ma-94	56	2	the	the	DET
ma-94	56	3	results	result	NOUN
ma-94	56	4	for	for	ADP
ma-94	56	5	the	the	DET
ma-94	56	6	chord	chord	NOUN
ma-94	56	7	method	method	NOUN
ma-94	56	8	can	can	AUX
ma-94	56	9	also	also	ADV
ma-94	56	10	be	be	AUX
ma-94	56	11	extended	extend	VERB
ma-94	56	12	.	.	PUNCT
ma-94	57	1	we	we	PRON
ma-94	57	2	leavethe	leavethe	VERB
ma-94	57	3	details	detail	NOUN
ma-94	57	4	to	to	ADP
ma-94	57	5	the	the	DET
ma-94	57	6	motivated	motivated	ADJ
ma-94	57	7	reader	reader	NOUN
ma-94	57	8	.	.	PUNCT
ma-94	58	1	for	for	ADP
ma-94	58	2	brevity	brevity	NOUN
ma-94	58	3	we	we	PRON
ma-94	58	4	skip	skip	VERB
ma-94	58	5	the	the	DET
ma-94	58	6	extensions	extension	NOUN
ma-94	58	7	on	on	ADP
ma-94	58	8	the	the	DET
ma-94	58	9	radii	radius	NOUN
ma-94	58	10	of	of	ADP
ma-94	58	11	convergenceballs	convergenceball	NOUN
ma-94	58	12	,	,	PUNCT
ma-94	58	13	and	and	CCONJ
ma-94	58	14	only	only	ADV
ma-94	58	15	mention	mention	VERB
ma-94	58	16	convergence	convergence	NOUN
ma-94	58	17	criteria	criterion	NOUN
ma-94	58	18	and	and	CCONJ
ma-94	58	19	error	error	NOUN
ma-94	58	20	estimates	estimate	NOUN
ma-94	58	21	.	.	PUNCT
ma-94	59	1	theorem	theorem	VERB
ma-94	59	2	2.5	2.5	NUM
ma-94	59	3	.	.	PUNCT
ma-94	60	1	assume	assume	VERB
ma-94	60	2	:	:	PUNCT
ma-94	60	3	hrλ	hrλ	X
ma-94	60	4	<	<	X
ma-94	60	5	1	1	NUM
ma-94	61	1	+	+	NUM
ma-94	61	2	λ	λ	PROPN
ma-94	61	3	2	2	NUM
ma-94	61	4	+	+	NUM
ma-94	61	5	λ	λ	NOUN
ma-94	61	6	,	,	PUNCT
ma-94	61	7	d	d	X
ma-94	61	8	≤	≤	X
ma-94	61	9	[	[	PUNCT
ma-94	61	10	1−	1−	NUM
ma-94	61	11	2	2	NUM
ma-94	61	12	+	+	CCONJ
ma-94	61	13	λ	λ	PROPN
ma-94	61	14	1	1	NUM
ma-94	61	15	+	+	NUM
ma-94	61	16	λ	λ	PROPN
ma-94	61	17	hrλ	hrλ	NOUN
ma-94	61	18	]	]	X
ma-94	62	1	λ	λ	X
ma-94	62	2	and	and	CCONJ
ma-94	62	3	ū(x0	ū(x0	ADV
ma-94	62	4	,	,	PUNCT
ma-94	62	5	r	r	NOUN
ma-94	62	6	)	)	PUNCT
ma-94	62	7	⊂	⊂	PROPN
ma-94	62	8	ω	ω	PROPN
ma-94	62	9	.	.	PUNCT
ma-94	63	1	then	then	ADV
ma-94	63	2	,	,	PUNCT
ma-94	63	3	limn−→∞	limn−→∞	PROPN
ma-94	63	4	xn	xn	PUNCT
ma-94	64	1	=	=	PUNCT
ma-94	64	2	x∗	x∗	PROPN
ma-94	64	3	∈	∈	PROPN
ma-94	64	4	u(x0	u(x0	NOUN
ma-94	64	5	,	,	PUNCT
ma-94	64	6	r0	r0	NOUN
ma-94	64	7	)	)	PUNCT
ma-94	64	8	and	and	CCONJ
ma-94	64	9	f	f	PROPN
ma-94	64	10	(	(	PUNCT
ma-94	64	11	x∗	x∗	PROPN
ma-94	64	12	)	)	PUNCT
ma-94	64	13	=	=	SYM
ma-94	64	14	0	0	X
ma-94	64	15	.	.	PUNCT
ma-94	65	1	furthermore	furthermore	ADV
ma-94	65	2	,	,	PUNCT
ma-94	65	3	‖x∗	‖x∗	PUNCT
ma-94	66	1	−	−	NOUN
ma-94	66	2	xn‖	xn‖	PROPN
ma-94	66	3	≤	≤	PROPN
ma-94	66	4	(	(	PUNCT
ma-94	66	5	µ	µ	X
ma-94	66	6	1	1	NUM
ma-94	66	7	λ	λ	SYM
ma-94	66	8	2	2	NUM
ma-94	66	9	+	+	NUM
ma-94	66	10	λ	λ	NOUN
ma-94	66	11	)	)	PUNCT
ma-94	66	12	(	(	PUNCT
ma-94	66	13	1+λ)p	1+λ)p	NUM
ma-94	66	14	r	r	NOUN
ma-94	66	15	µ	µ	NUM
ma-94	66	16	1	1	NUM
ma-94	66	17	λ	λ	NOUN
ma-94	66	18	,	,	PUNCT
ma-94	66	19	where	where	SCONJ
ma-94	66	20	µ	µ	X
ma-94	66	21	=	=	SYM
ma-94	66	22	hrλ	hrλ	NOUN
ma-94	66	23	1−h0rλ	1−h0rλ	NUM
ma-94	66	24	1	1	NUM
ma-94	66	25	1+λ	1+λ	NUM
ma-94	66	26	<	<	X
ma-94	66	27	1	1	X
ma-94	66	28	.	.	PUNCT
ma-94	66	29	proof	proof	NOUN
ma-94	66	30	.	.	PUNCT
ma-94	67	1	see	see	VERB
ma-94	67	2	theorem	theorem	NOUN
ma-94	67	3	2	2	NUM
ma-94	67	4	in	in	ADP
ma-94	67	5	[	[	PUNCT
ma-94	67	6	11	11	NUM
ma-94	67	7	]	]	PUNCT
ma-94	67	8	.	.	PUNCT
ma-94	68	1	�	�	PROPN
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ma-94	68	3	eur	eur	PROPN
ma-94	68	4	.	.	PUNCT
ma-94	69	1	j.	j.	PROPN
ma-94	69	2	math	math	PROPN
ma-94	69	3	.	.	PUNCT
ma-94	70	1	anal	anal	PROPN
ma-94	70	2	.	.	PUNCT
ma-94	71	1	10.28924	10.28924	NUM
ma-94	71	2	/	/	SYM
ma-94	71	3	ada	ada	PROPN
ma-94	71	4	/	/	SYM
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ma-94	71	6	4	4	NUM
ma-94	71	7	theorem	theorem	VERB
ma-94	71	8	2.6	2.6	NUM
ma-94	71	9	.	.	PUNCT
ma-94	72	1	assume	assume	VERB
ma-94	72	2	:	:	PUNCT
ma-94	72	3	hdλ	hdλ	NOUN
ma-94	72	4	<	<	X
ma-94	72	5	1	1	NUM
ma-94	72	6	2	2	NUM
ma-94	72	7	+	+	NUM
ma-94	72	8	λ	λ	PROPN
ma-94	72	9	(	(	PUNCT
ma-94	72	10	λ	λ	PROPN
ma-94	72	11	1	1	NUM
ma-94	72	12	+	+	NUM
ma-94	72	13	λ	λ	NOUN
ma-94	72	14	)	)	PUNCT
ma-94	72	15	λ	λ	PROPN
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ma-94	72	17	ū(x0	ū(x0	ADV
ma-94	72	18	,	,	PUNCT
ma-94	73	1	r	r	NOUN
ma-94	73	2	)	)	PUNCT
ma-94	73	3	⊂	⊂	PROPN
ma-94	73	4	ω	ω	PROPN
ma-94	73	5	.	.	PUNCT
ma-94	74	1	then	then	ADV
ma-94	74	2	,	,	PUNCT
ma-94	74	3	limn−→∞	limn−→∞	PROPN
ma-94	74	4	xn	xn	PUNCT
ma-94	75	1	=	=	PUNCT
ma-94	75	2	x∗	x∗	PROPN
ma-94	75	3	∈	∈	PROPN
ma-94	75	4	u(x0	u(x0	NOUN
ma-94	75	5	,	,	PUNCT
ma-94	75	6	r0	r0	NOUN
ma-94	75	7	)	)	PUNCT
ma-94	75	8	,	,	PUNCT
ma-94	75	9	f	f	PROPN
ma-94	75	10	(	(	PUNCT
ma-94	75	11	x∗	x∗	PROPN
ma-94	75	12	)	)	PUNCT
ma-94	75	13	=	=	SYM
ma-94	75	14	0	0	NUM
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ma-94	75	16	‖x∗	‖x∗	NUM
ma-94	76	1	−	−	NOUN
ma-94	76	2	xn‖	xn‖	PROPN
ma-94	76	3	≤	≤	PROPN
ma-94	76	4	(	(	PUNCT
ma-94	76	5	λ	λ	X
ma-94	76	6	1	1	NUM
ma-94	76	7	p	p	NOUN
ma-94	76	8	1−	1−	NUM
ma-94	76	9	λ	λ	NOUN
ma-94	76	10	)	)	PUNCT
ma-94	76	11	(	(	PUNCT
ma-94	76	12	1+p)n	1+p)n	NUM
ma-94	76	13	d	d	PROPN
ma-94	76	14	µ	µ	X
ma-94	76	15	1	1	NUM
ma-94	76	16	p	p	NOUN
ma-94	76	17	,	,	PUNCT
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ma-94	76	19	λ	λ	PROPN
ma-94	76	20	=	=	SYM
ma-94	76	21	hrp0	hrp0	PROPN
ma-94	76	22	1−h0rp0	1−h0rp0	NUM
ma-94	76	23	(	(	PUNCT
ma-94	76	24	d	d	NOUN
ma-94	76	25	r0	r0	NOUN
ma-94	76	26	)	)	PUNCT
ma-94	76	27	p	p	PART
ma-94	76	28	1	1	NUM
ma-94	76	29	1+p	1+p	NUM
ma-94	76	30	<	<	X
ma-94	76	31	1	1	NUM
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ma-94	76	33	r0	r0	NOUN
ma-94	76	34	is	be	AUX
ma-94	76	35	the	the	DET
ma-94	76	36	minimal	minimal	ADJ
ma-94	76	37	positive	positive	ADJ
ma-94	76	38	root	root	NOUN
ma-94	76	39	of	of	ADP
ma-94	76	40	scalar	scalar	ADJ
ma-94	76	41	equation	equation	NOUN
ma-94	76	42	(	(	PUNCT
ma-94	76	43	2	2	NUM
ma-94	76	44	+	+	NUM
ma-94	76	45	p)ht1+p	p)ht1+p	NOUN
ma-94	76	46	−	−	NOUN
ma-94	76	47	(	(	PUNCT
ma-94	76	48	1	1	NUM
ma-94	76	49	+	+	NUM
ma-94	76	50	p)(t	p)(t	PROPN
ma-94	76	51	−	−	NOUN
ma-94	76	52	d	d	NOUN
ma-94	76	53	)	)	PUNCT
ma-94	76	54	=	=	SYM
ma-94	76	55	0	0	NUM
ma-94	76	56	provided	provide	VERB
ma-94	76	57	that	that	SCONJ
ma-94	76	58	r	r	NOUN
ma-94	76	59	≥	≥	NOUN
ma-94	76	60	r0	r0	NOUN
ma-94	76	61	.	.	PUNCT
ma-94	77	1	proof	proof	NOUN
ma-94	77	2	.	.	PUNCT
ma-94	78	1	see	see	VERB
ma-94	78	2	theorem	theorem	VERB
ma-94	78	3	4	4	NUM
ma-94	78	4	in	in	ADP
ma-94	78	5	[	[	X
ma-94	78	6	11	11	NUM
ma-94	78	7	]	]	PUNCT
ma-94	78	8	.	.	PUNCT
ma-94	79	1	�	�	PROPN
ma-94	79	2	theorem	theorem	VERB
ma-94	79	3	2.7	2.7	NUM
ma-94	79	4	.	.	PUNCT
ma-94	80	1	assume	assume	VERB
ma-94	80	2	:	:	PUNCT
ma-94	80	3	hdp	hdp	PROPN
ma-94	80	4	≤	≤	PROPN
ma-94	80	5	1−	1−	NUM
ma-94	81	1	(	(	PUNCT
ma-94	81	2	p	p	NOUN
ma-94	81	3	1	1	NUM
ma-94	81	4	+	+	CCONJ
ma-94	81	5	p	p	NOUN
ma-94	81	6	)	)	PUNCT
ma-94	81	7	p	p	NOUN
ma-94	81	8	,	,	PUNCT
ma-94	81	9	r	r	NOUN
ma-94	81	10	≥	≥	NOUN
ma-94	81	11	1	1	NUM
ma-94	81	12	+	+	CCONJ
ma-94	81	13	p	p	NOUN
ma-94	81	14	2	2	NUM
ma-94	81	15	+	+	CCONJ
ma-94	81	16	p	p	NOUN
ma-94	81	17	−	−	PROPN
ma-94	81	18	(	(	PUNCT
ma-94	81	19	1	1	NUM
ma-94	81	20	+	+	NUM
ma-94	81	21	p)p	p)p	ADJ
ma-94	81	22	d	d	NOUN
ma-94	81	23	and	and	CCONJ
ma-94	81	24	ū(x0	ū(x0	ADV
ma-94	81	25	,	,	PUNCT
ma-94	81	26	r	r	NOUN
ma-94	81	27	)	)	PUNCT
ma-94	81	28	⊂	⊂	PROPN
ma-94	81	29	ω	ω	PROPN
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ma-94	82	1	then	then	ADV
ma-94	82	2	,	,	PUNCT
ma-94	82	3	limn−→∞	limn−→∞	PROPN
ma-94	82	4	xn	xn	PUNCT
ma-94	83	1	=	=	PUNCT
ma-94	83	2	x∗	x∗	PROPN
ma-94	83	3	∈	∈	PROPN
ma-94	83	4	u(x0	u(x0	NOUN
ma-94	83	5	,	,	PUNCT
ma-94	83	6	r	r	NOUN
ma-94	83	7	)	)	PUNCT
ma-94	83	8	,	,	PUNCT
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ma-94	83	10	(	(	PUNCT
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ma-94	83	13	=	=	SYM
ma-94	83	14	0	0	NUM
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ma-94	83	16	‖x∗	‖x∗	NUM
ma-94	84	1	−	−	NOUN
ma-94	84	2	xn‖	xn‖	PROPN
ma-94	84	3	≤	≤	PROPN
ma-94	84	4	(	(	PUNCT
ma-94	84	5	1	1	NUM
ma-94	84	6	1	1	NUM
ma-94	84	7	+	+	CCONJ
ma-94	84	8	p	p	NOUN
ma-94	84	9	)	)	PUNCT
ma-94	84	10	n	n	CCONJ
ma-94	84	11	[	[	X
ma-94	84	12	(	(	PUNCT
ma-94	84	13	1	1	NUM
ma-94	84	14	+	+	NUM
ma-94	84	15	p)h	p)h	NOUN
ma-94	84	16	1	1	NUM
ma-94	84	17	p	p	NOUN
ma-94	84	18	d	d	X
ma-94	84	19	]	]	X
ma-94	84	20	(	(	PUNCT
ma-94	84	21	1+p	1+p	NOUN
ma-94	84	22	)	)	PUNCT
ma-94	85	1	n	n	NOUN
ma-94	85	2	h	h	NOUN
ma-94	85	3	1	1	NUM
ma-94	85	4	p	p	NOUN
ma-94	85	5	.	.	PUNCT
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ma-94	86	2	.	.	PUNCT
ma-94	87	1	see	see	VERB
ma-94	87	2	theorem	theorem	VERB
ma-94	87	3	5	5	NUM
ma-94	87	4	in	in	ADP
ma-94	87	5	[	[	PUNCT
ma-94	87	6	11	11	NUM
ma-94	87	7	]	]	PUNCT
ma-94	87	8	.	.	PUNCT
ma-94	88	1	�	�	PROPN
ma-94	88	2	next	next	ADV
ma-94	88	3	,	,	PUNCT
ma-94	88	4	we	we	PRON
ma-94	88	5	extend	extend	VERB
ma-94	88	6	a	a	DET
ma-94	88	7	result	result	NOUN
ma-94	88	8	given	give	VERB
ma-94	88	9	in	in	ADP
ma-94	88	10	[	[	X
ma-94	88	11	6	6	NUM
ma-94	88	12	]	]	PUNCT
ma-94	88	13	which	which	PRON
ma-94	88	14	in	in	ADP
ma-94	88	15	turn	turn	NOUN
ma-94	88	16	extended	extend	VERB
ma-94	88	17	earlier	early	ADJ
ma-94	88	18	ones	one	NOUN
ma-94	88	19	[	[	X
ma-94	88	20	1,7–14	1,7–14	NUM
ma-94	88	21	]	]	PUNCT
ma-94	88	22	.	.	PUNCT
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ma-94	89	2	is	be	AUX
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ma-94	89	5	function	function	NOUN
ma-94	89	6	on	on	ADP
ma-94	89	7	the	the	DET
ma-94	89	8	interval	interval	NOUN
ma-94	89	9	[	[	X
ma-94	89	10	0,∞	0,∞	NOUN
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ma-94	91	7	d	d	X
ma-94	91	8	gβ(t	gβ(t	NOUN
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ma-94	93	1	+	+	CCONJ
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ma-94	93	5	t	t	NOUN
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ma-94	94	6	0	0	NUM
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ma-94	94	8	h(t	h(t	PROPN
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ma-94	94	10	=	=	SYM
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ma-94	94	12	+	+	CCONJ
ma-94	94	13	(	(	PUNCT
ma-94	94	14	1	1	NUM
ma-94	94	15	+	+	CCONJ
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ma-94	94	17	(	(	PUNCT
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ma-94	94	19	+	+	NUM
ma-94	94	20	p)1+p	p)1+p	NOUN
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ma-94	94	22	1	1	NUM
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ma-94	95	3	1	1	NUM
ma-94	95	4	:	:	PUNCT
ma-94	95	5	max	max	PROPN
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ma-94	95	17	}	}	PUNCT
ma-94	95	18	https://doi.org/10.28924/ada/ma.2.18	https://doi.org/10.28924/ada/ma.2.18	PROPN
ma-94	95	19	eur	eur	PROPN
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ma-94	96	1	j.	j.	PROPN
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ma-94	97	2	.	.	PUNCT
ma-94	98	1	10.28924	10.28924	NUM
ma-94	98	2	/	/	SYM
ma-94	98	3	ada	ada	PROPN
ma-94	98	4	/	/	SYM
ma-94	98	5	ma.2.18	ma.2.18	PROPN
ma-94	98	6	5and	5and	NUM
ma-94	98	7	scalar	scalar	ADJ
ma-94	98	8	sequence	sequence	NOUN
ma-94	98	9	{	{	PUNCT
ma-94	98	10	sn	sn	NOUN
ma-94	98	11	}	}	PUNCT
ma-94	98	12	by	by	ADP
ma-94	98	13	s0	s0	PROPN
ma-94	98	14	=	=	SYM
ma-94	98	15	0	0	NUM
ma-94	98	16	,	,	PUNCT
ma-94	98	17	sn	sn	NOUN
ma-94	98	18	=	=	PUNCT
ma-94	98	19	sn−1	sn−1	PROPN
ma-94	98	20	−	−	PROPN
ma-94	98	21	gd(sn−1	gd(sn−1	X
ma-94	98	22	)	)	PUNCT
ma-94	98	23	g′(sn−1	g′(sn−1	PROPN
ma-94	98	24	)	)	PUNCT
ma-94	98	25	.	.	PUNCT
ma-94	99	1	then	then	ADV
ma-94	99	2	,	,	PUNCT
ma-94	99	3	we	we	PRON
ma-94	99	4	can	can	AUX
ma-94	99	5	show	show	VERB
ma-94	99	6	:	:	PUNCT
ma-94	99	7	theorem	theorem	ADJ
ma-94	99	8	2.8	2.8	NUM
ma-94	99	9	.	.	PUNCT
ma-94	100	1	assume	assume	VERB
ma-94	100	2	:	:	PUNCT
ma-94	100	3	d	d	X
ma-94	100	4	≤	≤	ADJ
ma-94	100	5	1	1	NUM
ma-94	100	6	v(p	v(p	NOUN
ma-94	100	7	)	)	PUNCT
ma-94	100	8	(	(	PUNCT
ma-94	100	9	p	p	NOUN
ma-94	100	10	1	1	NUM
ma-94	100	11	+	+	CCONJ
ma-94	100	12	p	p	NOUN
ma-94	100	13	)	)	PUNCT
ma-94	100	14	p	p	NOUN
ma-94	100	15	and	and	CCONJ
ma-94	100	16	u(x0	u(x0	NOUN
ma-94	100	17	,	,	PUNCT
ma-94	100	18	r̄	r̄	NOUN
ma-94	100	19	)	)	PUNCT
ma-94	100	20	⊆	⊆	NUM
ma-94	100	21	ω	ω	NUM
ma-94	100	22	,	,	PUNCT
ma-94	100	23	where	where	SCONJ
ma-94	100	24	r̄	r̄	NOUN
ma-94	100	25	is	be	AUX
ma-94	100	26	the	the	DET
ma-94	100	27	minimal	minimal	ADJ
ma-94	100	28	solution	solution	NOUN
ma-94	100	29	of	of	ADP
ma-94	100	30	equation	equation	NOUN
ma-94	100	31	gv	gv	ADP
ma-94	100	32	(	(	PUNCT
ma-94	100	33	p	p	X
ma-94	100	34	)	)	PUNCT
ma-94	100	35	=	=	SYM
ma-94	100	36	0	0	NUM
ma-94	100	37	,	,	PUNCT
ma-94	100	38	gv	gv	X
ma-94	100	39	(	(	PUNCT
ma-94	100	40	t	t	NOUN
ma-94	100	41	)	)	PUNCT
ma-94	100	42	=	=	SYM
ma-94	100	43	v(p)h	v(p)h	NOUN
ma-94	100	44	1	1	NUM
ma-94	100	45	+	+	CCONJ
ma-94	100	46	p	p	X
ma-94	100	47	t1+p	t1+p	NOUN
ma-94	100	48	−	−	PROPN
ma-94	100	49	t	t	PROPN
ma-94	100	50	+	+	CCONJ
ma-94	100	51	d.	d.	PROPN
ma-94	100	52	proof	proof	NOUN
ma-94	100	53	.	.	PUNCT
ma-94	101	1	see	see	AUX
ma-94	101	2	theorem	theorem	VERB
ma-94	101	3	2.2	2.2	NUM
ma-94	101	4	in	in	ADP
ma-94	101	5	[	[	X
ma-94	101	6	6	6	NUM
ma-94	101	7	]	]	PUNCT
ma-94	101	8	.	.	PUNCT
ma-94	102	1	�	�	PROPN
ma-94	102	2	next	next	ADV
ma-94	102	3	,	,	PUNCT
ma-94	102	4	we	we	PRON
ma-94	102	5	present	present	VERB
ma-94	102	6	the	the	DET
ma-94	102	7	extensions	extension	NOUN
ma-94	102	8	of	of	ADP
ma-94	102	9	the	the	DET
ma-94	102	10	work	work	NOUN
ma-94	102	11	by	by	ADP
ma-94	102	12	rokne	rokne	NOUN
ma-94	102	13	in	in	ADP
ma-94	102	14	[	[	X
ma-94	102	15	13	13	NUM
ma-94	102	16	]	]	PUNCT
ma-94	102	17	but	but	CCONJ
ma-94	102	18	for	for	ADP
ma-94	102	19	the	the	DET
ma-94	102	20	newton	newton	PROPN
ma-94	102	21	-	-	PUNCT
ma-94	102	22	like	like	ADJ
ma-94	102	23	method(nlm	method(nlm	NOUN
ma-94	102	24	)	)	PUNCT
ma-94	102	25	xn+1	xn+1	PROPN
ma-94	103	1	=	=	SYM
ma-94	103	2	xn	xn	PROPN
ma-94	104	1	−	−	NOUN
ma-94	105	1	l−1n	l−1n	X
ma-94	105	2	f	f	X
ma-94	105	3	(	(	PUNCT
ma-94	105	4	xn	xn	PROPN
ma-94	105	5	)	)	PUNCT
ma-94	105	6	,	,	PUNCT
ma-94	105	7	where	where	SCONJ
ma-94	105	8	ln	ln	ADV
ma-94	105	9	is	be	AUX
ma-94	105	10	a	a	DET
ma-94	105	11	linear	linear	ADJ
ma-94	105	12	operator	operator	NOUN
ma-94	105	13	approximating	approximate	VERB
ma-94	105	14	f	f	PROPN
ma-94	105	15	′(xn	′(xn	PROPN
ma-94	105	16	)	)	PUNCT
ma-94	105	17	.	.	PUNCT
ma-94	106	1	theorem	theorem	VERB
ma-94	106	2	2.9	2.9	NUM
ma-94	106	3	.	.	PUNCT
ma-94	107	1	assume	assume	VERB
ma-94	107	2	:	:	PUNCT
ma-94	107	3	‖l(x)−	‖l(x)−	PROPN
ma-94	107	4	l(x0)‖	l(x0)‖	PROPN
ma-94	107	5	≤	≤	NUM
ma-94	107	6	m0‖x	m0‖x	NUM
ma-94	107	7	−	−	NUM
ma-94	107	8	x0‖p	x0‖p	NUM
ma-94	107	9	for	for	ADP
ma-94	107	10	all	all	DET
ma-94	107	11	x	x	SYM
ma-94	107	12	∈	∈	PROPN
ma-94	107	13	ω	ω	PROPN
ma-94	107	14	.	.	PUNCT
ma-94	108	1	set	set	VERB
ma-94	108	2	ω0	ω0	NOUN
ma-94	108	3	=	=	SYM
ma-94	108	4	u(x0	u(x0	NOUN
ma-94	108	5	,	,	PUNCT
ma-94	108	6	1	1	NUM
ma-94	108	7	(	(	PUNCT
ma-94	108	8	γ2m0	γ2m0	NOUN
ma-94	108	9	)	)	PUNCT
ma-94	108	10	1	1	NUM
ma-94	108	11	p	p	NOUN
ma-94	108	12	)	)	PUNCT
ma-94	108	13	.	.	PUNCT
ma-94	109	1	‖f	‖f	ADP
ma-94	109	2	′(x)−	′(x)−	NOUN
ma-94	109	3	f	f	PROPN
ma-94	109	4	′(y)‖	′(y)‖	PROPN
ma-94	109	5	≤	≤	PROPN
ma-94	109	6	m̄‖x	m̄‖x	X
ma-94	109	7	−	−	NOUN
ma-94	109	8	y‖p	y‖p	NOUN
ma-94	109	9	for	for	ADP
ma-94	109	10	all	all	DET
ma-94	109	11	x	x	NOUN
ma-94	109	12	,	,	PUNCT
ma-94	109	13	y	y	PROPN
ma-94	109	14	∈	∈	PROPN
ma-94	109	15	ω0	ω0	NOUN
ma-94	109	16	,	,	PUNCT
ma-94	109	17	‖f	‖f	ADP
ma-94	109	18	′(x)−	′(x)−	NOUN
ma-94	109	19	l(x)‖	l(x)‖	NOUN
ma-94	109	20	≤	≤	NUM
ma-94	109	21	γ0	γ0	NOUN
ma-94	109	22	+	+	CCONJ
ma-94	109	23	γ1‖x	γ1‖x	PROPN
ma-94	109	24	−	−	NUM
ma-94	109	25	x0‖p	x0‖p	NUM
ma-94	109	26	for	for	ADP
ma-94	109	27	all	all	DET
ma-94	109	28	x	x	SYM
ma-94	109	29	∈	∈	PROPN
ma-94	109	30	ω0	ω0	NOUN
ma-94	109	31	,	,	PUNCT
ma-94	109	32	and	and	CCONJ
ma-94	109	33	some	some	DET
ma-94	109	34	γ0	γ0	NOUN
ma-94	109	35	≥	≥	NOUN
ma-94	109	36	0	0	NUM
ma-94	109	37	,	,	PUNCT
ma-94	109	38	γ1	γ1	NOUN
ma-94	109	39	≥	≥	NOUN
ma-94	109	40	0	0	NUM
ma-94	109	41	.	.	PUNCT
ma-94	109	42	l(x0	l(x0	PROPN
ma-94	109	43	)	)	PUNCT
ma-94	109	44	−1	−1	NOUN
ma-94	109	45	∈	∈	PROPN
ma-94	109	46	l(y	l(y	PROPN
ma-94	109	47	,	,	PUNCT
ma-94	109	48	x	x	X
ma-94	109	49	)	)	PUNCT
ma-94	109	50	with	with	ADP
ma-94	109	51	‖l(x0	‖l(x0	PROPN
ma-94	109	52	)	)	PUNCT
ma-94	109	53	−1‖	−1‖	PROPN
ma-94	109	54	≤	≤	NOUN
ma-94	109	55	γ2	γ2	NOUN
ma-94	109	56	and	and	CCONJ
ma-94	109	57	‖l(x0	‖l(x0	ADJ
ma-94	109	58	)	)	PUNCT
ma-94	109	59	−1f	−1f	PROPN
ma-94	109	60	(	(	PUNCT
ma-94	109	61	x0)‖	x0)‖	PROPN
ma-94	109	62	≤	≤	NUM
ma-94	109	63	γ3	γ3	NOUN
ma-94	109	64	,	,	PUNCT
ma-94	109	65	function	function	NOUN
ma-94	109	66	q	q	PUNCT
ma-94	109	67	defined	define	VERB
ma-94	109	68	by	by	ADP
ma-94	109	69	q(t	q(t	NOUN
ma-94	109	70	)	)	PUNCT
ma-94	109	71	=	=	SYM
ma-94	109	72	t1+p(γ2γ0	t1+p(γ2γ0	PROPN
ma-94	109	73	+	+	CCONJ
ma-94	109	74	γ2m0	γ2m0	NOUN
ma-94	109	75	)	)	PUNCT
ma-94	109	76	+	+	SYM
ma-94	109	77	t	t	X
ma-94	109	78	(	(	PUNCT
ma-94	109	79	γ2m̄d	γ2m̄d	PROPN
ma-94	109	80	p	p	NOUN
ma-94	109	81	1	1	NUM
ma-94	110	1	+	+	CCONJ
ma-94	110	2	p	p	NOUN
ma-94	111	1	+	+	CCONJ
ma-94	111	2	γ2γ0	γ2γ0	ADP
ma-94	111	3	−	−	PROPN
ma-94	111	4	1)−	1)−	PROPN
ma-94	112	1	γ2m0γ3tp	γ2m0γ3tp	ADP
ma-94	112	2	+	+	NOUN
ma-94	112	3	γ3	γ3	NOUN
ma-94	112	4	has	have	VERB
ma-94	112	5	a	a	DET
ma-94	112	6	smallest	small	ADJ
ma-94	112	7	positive	positive	ADJ
ma-94	112	8	zero	zero	NUM
ma-94	112	9	r	r	NOUN
ma-94	112	10	>	>	X
ma-94	112	11	γ3	γ3	NOUN
ma-94	112	12	,	,	PUNCT
ma-94	112	13	γ2m̄r	γ2m̄r	PROPN
ma-94	112	14	p	p	X
ma-94	112	15	<	<	X
ma-94	112	16	1	1	NUM
ma-94	112	17	,	,	PUNCT
ma-94	112	18	ρ	ρ	PROPN
ma-94	112	19	=	=	SYM
ma-94	112	20	p	p	X
ma-94	112	21	1−	1−	NUM
ma-94	112	22	γ2m̄rp	γ2m̄rp	PROPN
ma-94	112	23	[	[	PUNCT
ma-94	112	24	γ2m̄d	γ2m̄d	X
ma-94	112	25	p	p	NOUN
ma-94	112	26	1	1	NUM
ma-94	112	27	+	+	CCONJ
ma-94	112	28	p	p	NOUN
ma-94	113	1	+	+	X
ma-94	113	2	γ2γ0	γ2γ0	ADP
ma-94	113	3	+	+	CCONJ
ma-94	113	4	γ2γ1r	γ2γ1r	X
ma-94	114	1	p	p	X
ma-94	114	2	]	]	PUNCT
ma-94	114	3	<	<	X
ma-94	114	4	1	1	NUM
ma-94	114	5	,	,	PUNCT
ma-94	114	6	ū(x0	ū(x0	ADV
ma-94	114	7	,	,	PUNCT
ma-94	114	8	r	r	NOUN
ma-94	114	9	)	)	PUNCT
ma-94	114	10	⊂	⊂	PROPN
ma-94	114	11	ω	ω	PROPN
ma-94	114	12	.	.	PUNCT
ma-94	115	1	then	then	ADV
ma-94	115	2	limn−→∞	limn−→∞	PROPN
ma-94	115	3	xn	xn	PROPN
ma-94	116	1	=	=	PUNCT
ma-94	116	2	x∗	x∗	PROPN
ma-94	116	3	and	and	CCONJ
ma-94	116	4	f	f	PROPN
ma-94	116	5	(	(	PUNCT
ma-94	116	6	x∗	x∗	PROPN
ma-94	116	7	)	)	PUNCT
ma-94	116	8	=	=	SYM
ma-94	117	1	0	0	X
ma-94	117	2	.	.	PUNCT
ma-94	118	1	https://doi.org/10.28924/ada/ma.2.18	https://doi.org/10.28924/ada/ma.2.18	PROPN
ma-94	118	2	eur	eur	PROPN
ma-94	118	3	.	.	PUNCT
ma-94	119	1	j.	j.	PROPN
ma-94	119	2	math	math	PROPN
ma-94	119	3	.	.	PUNCT
ma-94	120	1	anal	anal	PROPN
ma-94	120	2	.	.	PUNCT
ma-94	121	1	10.28924	10.28924	NUM
ma-94	121	2	/	/	SYM
ma-94	121	3	ada	ada	PROPN
ma-94	121	4	/	/	SYM
ma-94	121	5	ma.2.18	ma.2.18	PROPN
ma-94	121	6	6	6	NUM
ma-94	121	7	proof	proof	NOUN
ma-94	121	8	.	.	PUNCT
ma-94	122	1	see	see	VERB
ma-94	122	2	theorem	theorem	NOUN
ma-94	122	3	1	1	NUM
ma-94	122	4	in	in	ADP
ma-94	122	5	[	[	PUNCT
ma-94	122	6	13	13	NUM
ma-94	122	7	]	]	PUNCT
ma-94	122	8	.	.	PUNCT
ma-94	123	1	�	�	NOUN
ma-94	123	2	many	many	ADJ
ma-94	123	3	results	result	NOUN
ma-94	123	4	on	on	ADP
ma-94	123	5	newton	newton	PROPN
ma-94	123	6	’s	’s	PART
ma-94	123	7	method	method	NOUN
ma-94	123	8	were	be	AUX
ma-94	123	9	also	also	ADV
ma-94	123	10	reported	report	VERB
ma-94	123	11	in	in	ADP
ma-94	123	12	the	the	DET
ma-94	123	13	elegant	elegant	ADJ
ma-94	123	14	book	book	NOUN
ma-94	123	15	in	in	ADP
ma-94	123	16	[	[	X
ma-94	123	17	9	9	NUM
ma-94	123	18	]	]	PUNCT
ma-94	123	19	.	.	PUNCT
ma-94	124	1	next	next	ADV
ma-94	124	2	,	,	PUNCT
ma-94	124	3	we	we	PRON
ma-94	124	4	showhow	showhow	VERB
ma-94	124	5	to	to	PART
ma-94	124	6	extend	extend	VERB
ma-94	124	7	one	one	NUM
ma-94	124	8	of	of	ADP
ma-94	124	9	them	they	PRON
ma-94	124	10	.	.	PUNCT
ma-94	125	1	the	the	DET
ma-94	125	2	details	detail	NOUN
ma-94	125	3	of	of	ADP
ma-94	125	4	how	how	SCONJ
ma-94	125	5	to	to	PART
ma-94	125	6	extend	extend	VERB
ma-94	125	7	the	the	DET
ma-94	125	8	result	result	NOUN
ma-94	125	9	of	of	ADP
ma-94	125	10	them	they	PRON
ma-94	125	11	are	be	AUX
ma-94	125	12	left	leave	VERB
ma-94	125	13	to	to	ADP
ma-94	125	14	the	the	DET
ma-94	125	15	motivatedreader	motivatedreader	NOUN
ma-94	125	16	.	.	PUNCT
ma-94	126	1	theorem	theorem	VERB
ma-94	126	2	2.10	2.10	NUM
ma-94	126	3	.	.	PUNCT
ma-94	127	1	suppose	suppose	VERB
ma-94	127	2	:	:	PUNCT
ma-94	127	3	conditions	condition	NOUN
ma-94	127	4	(	(	PUNCT
ma-94	127	5	2.1	2.1	NUM
ma-94	127	6	)	)	PUNCT
ma-94	127	7	,	,	PUNCT
ma-94	127	8	(	(	PUNCT
ma-94	127	9	2.3	2.3	NUM
ma-94	127	10	)	)	PUNCT
ma-94	127	11	,	,	PUNCT
ma-94	127	12	(	(	PUNCT
ma-94	127	13	2.8	2.8	NUM
ma-94	127	14	)	)	PUNCT
ma-94	127	15	,	,	PUNCT
ma-94	127	16	and	and	CCONJ
ma-94	127	17	(	(	PUNCT
ma-94	127	18	c	c	X
ma-94	127	19	)	)	PUNCT
ma-94	127	20	h0	h0	NOUN
ma-94	127	21	=	=	PROPN
ma-94	127	22	hdp	hdp	PROPN
ma-94	127	23	∈	∈	PROPN
ma-94	127	24	(	(	PUNCT
ma-94	127	25	0	0	NUM
ma-94	127	26	,	,	PUNCT
ma-94	127	27	ρ	ρ	NOUN
ma-94	127	28	)	)	PUNCT
ma-94	127	29	where	where	SCONJ
ma-94	127	30	ρ	ρ	PROPN
ma-94	127	31	is	be	AUX
ma-94	127	32	the	the	DET
ma-94	127	33	only	only	ADJ
ma-94	127	34	solution	solution	NOUN
ma-94	127	35	of	of	ADP
ma-94	127	36	equation	equation	NOUN
ma-94	127	37	(	(	PUNCT
ma-94	127	38	1	1	NUM
ma-94	127	39	+	+	NUM
ma-94	127	40	p)p(1−	p)p(1−	PROPN
ma-94	127	41	t)1+p	t)1+p	NOUN
ma-94	127	42	−	−	NOUN
ma-94	127	43	tp	tp	NOUN
ma-94	127	44	=	=	SYM
ma-94	127	45	0	0	NUM
ma-94	127	46	,	,	PUNCT
ma-94	127	47	p	p	PROPN
ma-94	127	48	∈	∈	PROPN
ma-94	127	49	(	(	PUNCT
ma-94	127	50	0	0	NUM
ma-94	127	51	,	,	PUNCT
ma-94	127	52	1	1	NUM
ma-94	127	53	]	]	PUNCT
ma-94	127	54	in	in	ADP
ma-94	127	55	(	(	PUNCT
ma-94	127	56	0	0	NUM
ma-94	127	57	,	,	PUNCT
ma-94	127	58	12	12	NUM
ma-94	127	59	]	]	PUNCT
ma-94	127	60	and	and	CCONJ
ma-94	127	61	u(x0	u(x0	NOUN
ma-94	127	62	,	,	PUNCT
ma-94	127	63	s	s	PART
ma-94	127	64	)	)	PUNCT
ma-94	127	65	⊂	⊂	PROPN
ma-94	127	66	ω	ω	PROPN
ma-94	127	67	,	,	PUNCT
ma-94	127	68	where	where	SCONJ
ma-94	127	69	s	s	VERB
ma-94	127	70	=	=	SYM
ma-94	127	71	(	(	PUNCT
ma-94	127	72	1+p)(1−h0	1+p)(1−h0	NUM
ma-94	127	73	)	)	PUNCT
ma-94	127	74	(	(	PUNCT
ma-94	127	75	1+p)−(2+p)h0	1+p)−(2+p)h0	NUM
ma-94	127	76	hold	hold	VERB
ma-94	127	77	.	.	PUNCT
ma-94	128	1	then	then	ADV
ma-94	128	2	,	,	PUNCT
ma-94	128	3	sequence	sequence	NOUN
ma-94	128	4	{	{	PUNCT
ma-94	128	5	xn	xn	NOUN
ma-94	128	6	}	}	PUNCT
ma-94	128	7	converges	converge	NOUN
ma-94	128	8	to	to	ADP
ma-94	128	9	a	a	DET
ma-94	128	10	solution	solution	NOUN
ma-94	128	11	x∗	x∗	NOUN
ma-94	128	12	of	of	ADP
ma-94	128	13	equation	equation	NOUN
ma-94	128	14	f	f	X
ma-94	128	15	(	(	PUNCT
ma-94	128	16	x	x	X
ma-94	128	17	)	)	PUNCT
ma-94	128	18	=	=	SYM
ma-94	129	1	0	0	X
ma-94	129	2	.	.	PUNCT
ma-94	130	1	moreover	moreover	ADV
ma-94	130	2	,	,	PUNCT
ma-94	130	3	{	{	PUNCT
ma-94	130	4	xn	xn	PUNCT
ma-94	130	5	}	}	PUNCT
ma-94	130	6	,	,	PUNCT
ma-94	130	7	x∗	x∗	PROPN
ma-94	130	8	∈	∈	PROPN
ma-94	130	9	u[x0	u[x0	NOUN
ma-94	130	10	,	,	PUNCT
ma-94	130	11	s	s	X
ma-94	130	12	]	]	PUNCT
ma-94	130	13	and	and	CCONJ
ma-94	130	14	x∗	x∗	PROPN
ma-94	130	15	is	be	AUX
ma-94	130	16	the	the	DET
ma-94	130	17	only	only	ADJ
ma-94	130	18	solution	solution	NOUN
ma-94	130	19	in	in	ADP
ma-94	130	20	ω	ω	PROPN
ma-94	130	21	∩	∩	NOUN
ma-94	130	22	u(x0	u(x0	NOUN
ma-94	130	23	,	,	PUNCT
ma-94	130	24	d	d	PROPN
ma-94	130	25	h	h	NOUN
ma-94	130	26	1	1	NUM
ma-94	130	27	/	/	SYM
ma-94	130	28	p	p	NOUN
ma-94	130	29	0	0	NUM
ma-94	130	30	)	)	PUNCT
ma-94	130	31	.	.	PUNCT
ma-94	131	1	moreover	moreover	ADV
ma-94	131	2	,	,	PUNCT
ma-94	131	3	the	the	DET
ma-94	131	4	following	follow	VERB
ma-94	131	5	error	error	NOUN
ma-94	131	6	estimates	estimate	NOUN
ma-94	131	7	hold	hold	VERB
ma-94	131	8	‖xn	‖xn	PROPN
ma-94	131	9	−	−	PROPN
ma-94	131	10	x∗‖	x∗‖	PROPN
ma-94	131	11	≤	≤	PROPN
ma-94	131	12	en	en	ADP
ma-94	131	13	,	,	PUNCT
ma-94	131	14	where	where	SCONJ
ma-94	131	15	en	en	PROPN
ma-94	131	16	=	=	SYM
ma-94	131	17	δ	δ	PROPN
ma-94	131	18	(	(	PUNCT
ma-94	131	19	1+p)n−1	1+p)n−1	NUM
ma-94	131	20	p2	p2	NOUN
ma-94	131	21	an	an	DET
ma-94	131	22	1−δ	1−δ	NUM
ma-94	131	23	(	(	PUNCT
ma-94	131	24	1+p)n	1+p)n	NUM
ma-94	131	25	p	p	NOUN
ma-94	131	26	a	a	DET
ma-94	131	27	d	d	NOUN
ma-94	131	28	,	,	PUNCT
ma-94	131	29	with	with	ADP
ma-94	131	30	δ	δ	PROPN
ma-94	131	31	=	=	PUNCT
ma-94	131	32	h1	h1	PROPN
ma-94	131	33	h0	h0	NOUN
ma-94	131	34	,	,	PUNCT
ma-94	131	35	a	a	DET
ma-94	131	36	=	=	SYM
ma-94	131	37	1	1	NUM
ma-94	131	38	−	−	PROPN
ma-94	131	39	h0	h0	PROPN
ma-94	131	40	,	,	PUNCT
ma-94	131	41	h1	h1	NOUN
ma-94	131	42	=	=	PUNCT
ma-94	131	43	h0f1(h0	h0f1(h0	NOUN
ma-94	131	44	)	)	PUNCT
ma-94	131	45	1+pf2(h0	1+pf2(h0	NUM
ma-94	131	46	)	)	PUNCT
ma-94	131	47	p	p	X
ma-94	131	48	,	,	PUNCT
ma-94	131	49	f1(t	f1(t	PROPN
ma-94	131	50	)	)	PUNCT
ma-94	131	51	=	=	SYM
ma-94	131	52	1	1	NUM
ma-94	131	53	1−t	1−t	NUM
ma-94	131	54	and	and	CCONJ
ma-94	131	55	f2(t	f2(t	PROPN
ma-94	131	56	)	)	PUNCT
ma-94	131	57	=	=	PUNCT
ma-94	131	58	t	t	PROPN
ma-94	131	59	1+p	1+p	NUM
ma-94	131	60	.	.	PUNCT
ma-94	132	1	finally	finally	ADV
ma-94	132	2	,	,	PUNCT
ma-94	132	3	we	we	PRON
ma-94	132	4	extend	extend	VERB
ma-94	132	5	the	the	DET
ma-94	132	6	results	result	NOUN
ma-94	132	7	by	by	ADP
ma-94	132	8	f.	f.	PROPN
ma-94	132	9	cianciaruso	cianciaruso	PROPN
ma-94	132	10	and	and	CCONJ
ma-94	132	11	e.	e.	PROPN
ma-94	132	12	de	de	PROPN
ma-94	132	13	pascale	pascale	PROPN
ma-94	132	14	in	in	ADP
ma-94	132	15	[	[	X
ma-94	132	16	6	6	NUM
ma-94	132	17	]	]	PUNCT
ma-94	132	18	who	who	PRON
ma-94	132	19	in	in	ADP
ma-94	132	20	turn	turn	NOUN
ma-94	132	21	extendedearlier	extendedearlier	NOUN
ma-94	132	22	ones	one	NOUN
ma-94	132	23	[	[	X
ma-94	132	24	1	1	NUM
ma-94	132	25	,	,	PUNCT
ma-94	132	26	5	5	NUM
ma-94	132	27	,	,	PUNCT
ma-94	132	28	7	7	NUM
ma-94	132	29	,	,	PUNCT
ma-94	132	30	11,12,14	11,12,14	NUM
ma-94	132	31	]	]	PUNCT
ma-94	132	32	.	.	PUNCT
ma-94	133	1	define	define	VERB
ma-94	133	2	scalar	scalar	ADJ
ma-94	133	3	sequence	sequence	NOUN
ma-94	133	4	{	{	PUNCT
ma-94	133	5	vn	vn	NOUN
ma-94	133	6	}	}	PUNCT
ma-94	133	7	for	for	ADP
ma-94	133	8	h	h	NOUN
ma-94	133	9	=	=	SYM
ma-94	133	10	dph	dph	PROPN
ma-94	133	11	by	by	ADP
ma-94	133	12	v0	v0	NOUN
ma-94	133	13	=	=	SYM
ma-94	133	14	0	0	NUM
ma-94	133	15	,	,	PUNCT
ma-94	133	16	v1	v1	NOUN
ma-94	133	17	=	=	SYM
ma-94	133	18	h	h	NOUN
ma-94	133	19	1	1	NUM
ma-94	133	20	p	p	NOUN
ma-94	133	21	,	,	PUNCT
ma-94	134	1	vn+1	vn+1	PROPN
ma-94	134	2	=	=	SYM
ma-94	134	3	vn	vn	PROPN
ma-94	135	1	+	+	CCONJ
ma-94	135	2	(	(	PUNCT
ma-94	135	3	vn	vn	INTJ
ma-94	135	4	−	−	PROPN
ma-94	135	5	vn−1)1+p	vn−1)1+p	PROPN
ma-94	135	6	(	(	PUNCT
ma-94	135	7	1	1	NUM
ma-94	135	8	+	+	NUM
ma-94	135	9	p)(1−	p)(1−	ADJ
ma-94	135	10	vpn	vpn	NOUN
ma-94	135	11	)	)	PUNCT
ma-94	135	12	.	.	PUNCT
ma-94	136	1	(	(	PUNCT
ma-94	136	2	2.12	2.12	NUM
ma-94	136	3	)	)	PUNCT
ma-94	136	4	next	next	ADV
ma-94	136	5	,	,	PUNCT
ma-94	136	6	we	we	PRON
ma-94	136	7	extend	extend	VERB
ma-94	136	8	theorem	theorem	VERB
ma-94	136	9	2.1	2.1	NUM
ma-94	136	10	and	and	CCONJ
ma-94	136	11	theorem	theorem	VERB
ma-94	136	12	2.3	2.3	NUM
ma-94	136	13	in	in	ADP
ma-94	136	14	[	[	X
ma-94	136	15	6	6	NUM
ma-94	136	16	]	]	PUNCT
ma-94	136	17	,	,	PUNCT
ma-94	136	18	respectively	respectively	ADV
ma-94	136	19	.	.	PUNCT
ma-94	137	1	theorem	theorem	VERB
ma-94	137	2	2.11	2.11	NUM
ma-94	137	3	.	.	PUNCT
ma-94	138	1	let	let	VERB
ma-94	138	2	function	function	VERB
ma-94	139	1	f	f	X
ma-94	139	2	:	:	PUNCT
ma-94	140	1	[	[	X
ma-94	140	2	1,∞	1,∞	NUM
ma-94	140	3	)	)	PUNCT
ma-94	140	4	−→	−→	NOUN
ma-94	140	5	[	[	X
ma-94	140	6	0,∞	0,∞	NOUN
ma-94	140	7	)	)	PUNCT
ma-94	140	8	,	,	PUNCT
ma-94	140	9	r	r	NOUN
ma-94	140	10	:	:	PUNCT
ma-94	141	1	[	[	X
ma-94	141	2	0,∞	0,∞	X
ma-94	141	3	)	)	PUNCT
ma-94	141	4	−→	−→	NOUN
ma-94	141	5	[	[	X
ma-94	141	6	0,∞	0,∞	NOUN
ma-94	141	7	)	)	PUNCT
ma-94	141	8	be	be	AUX
ma-94	141	9	defined	define	VERB
ma-94	141	10	by	by	ADP
ma-94	141	11	f	f	PROPN
ma-94	141	12	(	(	PUNCT
ma-94	141	13	t	t	PROPN
ma-94	141	14	)	)	PUNCT
ma-94	141	15	=	=	PUNCT
ma-94	142	1	(	(	PUNCT
ma-94	142	2	1−	1−	NUM
ma-94	142	3	1	1	NUM
ma-94	142	4	t	t	NOUN
ma-94	142	5	)	)	PUNCT
ma-94	142	6	1	1	NUM
ma-94	143	1	+	+	CCONJ
ma-94	143	2	p	p	X
ma-94	143	3	(	(	PUNCT
ma-94	143	4	(	(	PUNCT
ma-94	143	5	1	1	NUM
ma-94	143	6	+	+	CCONJ
ma-94	143	7	p	p	X
ma-94	143	8	)	)	PUNCT
ma-94	143	9	1	1	NUM
ma-94	143	10	1−p	1−p	NUM
ma-94	143	11	+	+	CCONJ
ma-94	143	12	(	(	PUNCT
ma-94	143	13	t(t	t(t	NOUN
ma-94	143	14	−	−	NOUN
ma-94	143	15	1)p	1)p	NUM
ma-94	143	16	)	)	PUNCT
ma-94	143	17	1	1	NUM
ma-94	143	18	1−p	1−p	NUM
ma-94	143	19	)	)	PUNCT
ma-94	143	20	1−p	1−p	NUM
ma-94	143	21	and	and	CCONJ
ma-94	143	22	r(t	r(t	NOUN
ma-94	143	23	)	)	PUNCT
ma-94	143	24	=	=	PUNCT
ma-94	144	1	(	(	PUNCT
ma-94	144	2	1	1	NUM
ma-94	144	3	+	+	CCONJ
ma-94	144	4	p	p	X
ma-94	144	5	)	)	PUNCT
ma-94	144	6	1	1	NUM
ma-94	144	7	p	p	NOUN
ma-94	144	8	(	(	PUNCT
ma-94	144	9	(	(	PUNCT
ma-94	144	10	1	1	NUM
ma-94	144	11	+	+	CCONJ
ma-94	144	12	p	p	X
ma-94	144	13	)	)	PUNCT
ma-94	144	14	1	1	NUM
ma-94	144	15	1−p	1−p	NUM
ma-94	144	16	+	+	CCONJ
ma-94	144	17	(	(	PUNCT
ma-94	144	18	t(t	t(t	NOUN
ma-94	144	19	−	−	NOUN
ma-94	144	20	1)p	1)p	NUM
ma-94	144	21	)	)	PUNCT
ma-94	144	22	1	1	NUM
ma-94	144	23	1−p	1−p	NUM
ma-94	144	24	)	)	PUNCT
ma-94	144	25	1−p	1−p	PROPN
ma-94	144	26	.	.	PUNCT
ma-94	144	27	suppose	suppose	VERB
ma-94	144	28	that	that	SCONJ
ma-94	144	29	h	h	PROPN
ma-94	144	30	≤	≤	X
ma-94	144	31	f	f	X
ma-94	144	32	(	(	PUNCT
ma-94	144	33	m	m	PROPN
ma-94	144	34	)	)	PUNCT
ma-94	144	35	,	,	PUNCT
ma-94	144	36	(	(	PUNCT
ma-94	144	37	2.13	2.13	NUM
ma-94	144	38	)	)	PUNCT
ma-94	144	39	where	where	SCONJ
ma-94	144	40	m	m	NOUN
ma-94	144	41	is	be	AUX
ma-94	144	42	a	a	DET
ma-94	144	43	global	global	ADJ
ma-94	144	44	maximum	maximum	NOUN
ma-94	144	45	for	for	ADP
ma-94	144	46	function	function	NOUN
ma-94	144	47	f	f	PROPN
ma-94	144	48	,	,	PUNCT
ma-94	144	49	given	give	VERB
ma-94	144	50	explicitly	explicitly	ADV
ma-94	144	51	by	by	ADP
ma-94	144	52	m	m	PROPN
ma-94	144	53	=	=	NOUN
ma-94	144	54	1	1	NUM
ma-94	144	55	+	+	NUM
ma-94	144	56	√	√	NUM
ma-94	144	57	1	1	NUM
ma-94	144	58	+	+	NOUN
ma-94	144	59	4(1+p)pp1−p	4(1+p)pp1−p	NUM
ma-94	144	60	2	2	NUM
ma-94	144	61	.	.	PUNCT
ma-94	145	1	then	then	ADV
ma-94	145	2	,	,	PUNCT
ma-94	145	3	the	the	DET
ma-94	145	4	following	follow	VERB
ma-94	145	5	assertion	assertion	NOUN
ma-94	145	6	hold	hold	VERB
ma-94	145	7	vn	vn	ADP
ma-94	145	8	≤	≤	NUM
ma-94	145	9	r(m)(1−	r(m)(1−	ADP
ma-94	145	10	1	1	NUM
ma-94	145	11	mn	mn	PROPN
ma-94	145	12	)	)	PUNCT
ma-94	145	13	,	,	PUNCT
ma-94	145	14	(	(	PUNCT
ma-94	145	15	2.14	2.14	NUM
ma-94	145	16	)	)	PUNCT
ma-94	145	17	vn+1	vn+1	PROPN
ma-94	145	18	vn	vn	VERB
ma-94	145	19	≤	≤	PROPN
ma-94	145	20	1−	1−	NUM
ma-94	145	21	1	1	NUM
ma-94	145	22	mn+1	mn+1	NOUN
ma-94	145	23	1−	1−	NUM
ma-94	145	24	1	1	NUM
ma-94	145	25	mn	mn	PROPN
ma-94	145	26	,	,	PUNCT
ma-94	145	27	(	(	PUNCT
ma-94	145	28	2.15	2.15	NUM
ma-94	145	29	)	)	PUNCT
ma-94	145	30	https://doi.org/10.28924/ada/ma.2.18	https://doi.org/10.28924/ada/ma.2.18	PROPN
ma-94	145	31	eur	eur	PROPN
ma-94	145	32	.	.	PUNCT
ma-94	146	1	j.	j.	PROPN
ma-94	146	2	math	math	PROPN
ma-94	146	3	.	.	PUNCT
ma-94	147	1	anal	anal	PROPN
ma-94	147	2	.	.	PUNCT
ma-94	148	1	10.28924	10.28924	NUM
ma-94	148	2	/	/	SYM
ma-94	148	3	ada	ada	PROPN
ma-94	148	4	/	/	SYM
ma-94	148	5	ma.2.18	ma.2.18	PROPN
ma-94	148	6	7	7	NUM
ma-94	148	7	vn	vn	PROPN
ma-94	148	8	≤	≤	PROPN
ma-94	148	9	vn+1	vn+1	PROPN
ma-94	148	10	≤	≤	NUM
ma-94	148	11	r(m	r(m	NOUN
ma-94	148	12	)	)	PUNCT
ma-94	148	13	<	<	X
ma-94	148	14	1	1	NUM
ma-94	148	15	and	and	CCONJ
ma-94	148	16	limn−→∞	limn−→∞	NOUN
ma-94	148	17	vn	vn	PROPN
ma-94	148	18	=	=	SYM
ma-94	148	19	v∗	v∗	PROPN
ma-94	148	20	∈	∈	PROPN
ma-94	149	1	[	[	X
ma-94	149	2	0	0	NUM
ma-94	149	3	,	,	PUNCT
ma-94	149	4	r(m	r(m	PROPN
ma-94	149	5	)	)	PUNCT
ma-94	149	6	]	]	PUNCT
ma-94	149	7	.	.	PUNCT
ma-94	150	1	simply	simply	ADV
ma-94	150	2	use	use	VERB
ma-94	150	3	h	h	NOUN
ma-94	150	4	for	for	ADP
ma-94	150	5	h1	h1	NOUN
ma-94	150	6	in	in	ADP
ma-94	150	7	[	[	X
ma-94	150	8	6	6	NUM
ma-94	150	9	]	]	PUNCT
ma-94	150	10	.	.	PUNCT
ma-94	151	1	�	�	PROPN
ma-94	151	2	theorem	theorem	VERB
ma-94	151	3	2.12	2.12	NUM
ma-94	151	4	.	.	PUNCT
ma-94	152	1	under	under	ADP
ma-94	152	2	condition	condition	NOUN
ma-94	152	3	(	(	PUNCT
ma-94	152	4	2.13	2.13	NUM
ma-94	152	5	)	)	PUNCT
ma-94	152	6	further	far	ADV
ma-94	152	7	suppose	suppose	VERB
ma-94	152	8	that	that	SCONJ
ma-94	152	9	r∗	r∗	PROPN
ma-94	152	10	=	=	PUNCT
ma-94	152	11	h−	h−	VERB
ma-94	152	12	1	1	NUM
ma-94	152	13	p	p	NOUN
ma-94	152	14	v∗	v∗	PROPN
ma-94	152	15	≤	≤	PROPN
ma-94	152	16	ρ	ρ	NOUN
ma-94	152	17	and	and	CCONJ
ma-94	152	18	u(x0	u(x0	NOUN
ma-94	152	19	,	,	PUNCT
ma-94	152	20	ρ	ρ	PROPN
ma-94	152	21	)	)	PUNCT
ma-94	152	22	⊆	⊆	NUM
ma-94	152	23	ω	ω	NOUN
ma-94	152	24	.	.	PUNCT
ma-94	153	1	then	then	ADV
ma-94	153	2	,	,	PUNCT
ma-94	153	3	sequence	sequence	NOUN
ma-94	153	4	{	{	PUNCT
ma-94	153	5	xn	xn	PROPN
ma-94	153	6	}	}	PUNCT
ma-94	153	7	generated	generate	VERB
ma-94	153	8	by	by	ADP
ma-94	153	9	nm	nm	NOUN
ma-94	153	10	is	be	AUX
ma-94	153	11	well	well	ADV
ma-94	153	12	defined	define	VERB
ma-94	153	13	in	in	ADP
ma-94	153	14	u(x0	u(x0	NOUN
ma-94	153	15	,	,	PUNCT
ma-94	153	16	v	v	NOUN
ma-94	153	17	∗	∗	NOUN
ma-94	153	18	)	)	PUNCT
ma-94	153	19	,	,	PUNCT
ma-94	153	20	stays	stay	VERB
ma-94	153	21	in	in	ADP
ma-94	153	22	u(x0	u(x0	NOUN
ma-94	153	23	,	,	PUNCT
ma-94	153	24	v	v	NOUN
ma-94	153	25	∗	∗	NOUN
ma-94	153	26	)	)	PUNCT
ma-94	153	27	and	and	CCONJ
ma-94	153	28	converges	converge	VERB
ma-94	153	29	to	to	ADP
ma-94	153	30	the	the	DET
ma-94	153	31	unique	unique	ADJ
ma-94	153	32	solution	solution	NOUN
ma-94	153	33	x∗	x∗	PROPN
ma-94	153	34	∈	∈	PROPN
ma-94	153	35	u[x0	u[x0	NOUN
ma-94	153	36	,	,	PUNCT
ma-94	153	37	v	v	ADP
ma-94	153	38	∗	∗	NOUN
ma-94	153	39	]	]	PUNCT
ma-94	153	40	of	of	ADP
ma-94	153	41	equation	equation	NOUN
ma-94	153	42	f	f	X
ma-94	153	43	(	(	PUNCT
ma-94	153	44	x	x	X
ma-94	153	45	)	)	PUNCT
ma-94	153	46	=	=	SYM
ma-94	153	47	0	0	NUM
ma-94	153	48	,	,	PUNCT
ma-94	153	49	so	so	SCONJ
ma-94	153	50	that	that	SCONJ
ma-94	153	51	‖xn+1	‖xn+1	X
ma-94	153	52	−	−	NOUN
ma-94	153	53	xn‖	xn‖	PROPN
ma-94	153	54	≤	≤	PROPN
ma-94	153	55	vn+1	vn+1	PROPN
ma-94	153	56	−	−	PROPN
ma-94	153	57	vn	vn	PROPN
ma-94	153	58	and	and	CCONJ
ma-94	153	59	‖x∗	‖x∗	NUM
ma-94	154	1	−	−	NOUN
ma-94	154	2	xn‖	xn‖	PROPN
ma-94	154	3	≤	≤	PROPN
ma-94	154	4	v∗	v∗	PROPN
ma-94	154	5	−	−	PROPN
ma-94	154	6	vn	vn	NOUN
ma-94	154	7	.	.	PUNCT
ma-94	155	1	proof	proof	NOUN
ma-94	155	2	.	.	PUNCT
ma-94	156	1	simply	simply	ADV
ma-94	156	2	use	use	VERB
ma-94	156	3	h	h	NOUN
ma-94	156	4	for	for	SCONJ
ma-94	156	5	h1	h1	NOUN
ma-94	156	6	used	use	VERB
ma-94	156	7	in	in	ADP
ma-94	156	8	[	[	X
ma-94	156	9	6	6	NUM
ma-94	156	10	]	]	PUNCT
ma-94	156	11	.	.	PUNCT
ma-94	157	1	remark	remark	PROPN
ma-94	157	2	2.13	2.13	NUM
ma-94	157	3	.	.	PUNCT
ma-94	158	1	(	(	PUNCT
ma-94	158	2	1	1	X
ma-94	158	3	)	)	PUNCT
ma-94	158	4	if	if	SCONJ
ma-94	158	5	k	k	PROPN
ma-94	158	6	=	=	PRON
ma-94	158	7	h1	h1	VERB
ma-94	158	8	the	the	DET
ma-94	158	9	last	last	ADJ
ma-94	158	10	two	two	NUM
ma-94	158	11	results	result	NOUN
ma-94	158	12	coincide	coincide	VERB
ma-94	158	13	with	with	ADP
ma-94	158	14	the	the	DET
ma-94	158	15	corresponding	correspond	VERB
ma-94	158	16	ones	one	NOUN
ma-94	158	17	in	in	ADP
ma-94	158	18	[	[	X
ma-94	158	19	6	6	NUM
ma-94	158	20	]	]	PUNCT
ma-94	158	21	.	.	PUNCT
ma-94	159	1	but	but	CCONJ
ma-94	159	2	if	if	SCONJ
ma-94	159	3	k	k	PROPN
ma-94	159	4	<	<	X
ma-94	159	5	h1	h1	PROPN
ma-94	159	6	then	then	ADV
ma-94	159	7	the	the	DET
ma-94	159	8	new	new	ADJ
ma-94	159	9	results	result	NOUN
ma-94	159	10	constitute	constitute	VERB
ma-94	159	11	an	an	DET
ma-94	159	12	improvement	improvement	NOUN
ma-94	159	13	with	with	ADP
ma-94	159	14	benefits	benefit	NOUN
ma-94	159	15	already	already	ADV
ma-94	159	16	stated	state	VERB
ma-94	159	17	in	in	ADP
ma-94	159	18	the	the	DET
ma-94	159	19	introduction	introduction	NOUN
ma-94	159	20	.	.	PUNCT
ma-94	160	1	notice	notice	VERB
ma-94	160	2	that	that	SCONJ
ma-94	160	3	the	the	DET
ma-94	160	4	majorizing	majorize	VERB
ma-94	160	5	sequence	sequence	NOUN
ma-94	160	6	{	{	PUNCT
ma-94	160	7	wn	wn	NOUN
ma-94	160	8	}	}	PUNCT
ma-94	160	9	in	in	ADP
ma-94	160	10	[	[	X
ma-94	160	11	6	6	NUM
ma-94	160	12	]	]	PUNCT
ma-94	160	13	was	be	AUX
ma-94	160	14	defined	define	VERB
ma-94	160	15	for	for	ADP
ma-94	160	16	h1	h1	NOUN
ma-94	160	17	=	=	SYM
ma-94	160	18	dph1	dph1	PROPN
ma-94	160	19	by	by	ADP
ma-94	160	20	w0	w0	PROPN
ma-94	160	21	=	=	SYM
ma-94	160	22	0	0	NUM
ma-94	160	23	,	,	PUNCT
ma-94	161	1	w1	w1	NOUN
ma-94	161	2	=	=	SYM
ma-94	161	3	h	h	NOUN
ma-94	161	4	1	1	NUM
ma-94	161	5	p	p	NOUN
ma-94	161	6	1	1	NUM
ma-94	161	7	,	,	PUNCT
ma-94	161	8	wn+1	wn+1	NOUN
ma-94	161	9	=	=	SYM
ma-94	161	10	wn	wn	PROPN
ma-94	162	1	+	+	CCONJ
ma-94	162	2	(	(	PUNCT
ma-94	162	3	wn	wn	PROPN
ma-94	162	4	−	−	PROPN
ma-94	162	5	wn−1)1+p	wn−1)1+p	PROPN
ma-94	162	6	(	(	PUNCT
ma-94	162	7	1	1	NUM
ma-94	162	8	+	+	CCONJ
ma-94	162	9	p)(1−	p)(1−	ADJ
ma-94	162	10	wpn	wpn	PROPN
ma-94	162	11	)	)	PUNCT
ma-94	162	12	,	,	PUNCT
ma-94	162	13	(	(	PUNCT
ma-94	162	14	2.16	2.16	NUM
ma-94	162	15	)	)	PUNCT
ma-94	162	16	and	and	CCONJ
ma-94	162	17	the	the	DET
ma-94	162	18	convergence	convergence	NOUN
ma-94	162	19	criterion	criterion	NOUN
ma-94	162	20	is	be	AUX
ma-94	162	21	h1	h1	VERB
ma-94	162	22	≤	≤	ADJ
ma-94	162	23	f	f	X
ma-94	162	24	(	(	PUNCT
ma-94	162	25	m	m	PROPN
ma-94	162	26	)	)	PUNCT
ma-94	162	27	.	.	PUNCT
ma-94	163	1	(	(	PUNCT
ma-94	163	2	2.17	2.17	NUM
ma-94	163	3	)	)	PUNCT
ma-94	163	4	it	it	PRON
ma-94	163	5	then	then	ADV
ma-94	163	6	follows	follow	VERB
ma-94	163	7	by	by	ADP
ma-94	163	8	(	(	PUNCT
ma-94	163	9	2.7	2.7	NUM
ma-94	163	10	)	)	PUNCT
ma-94	163	11	,	,	PUNCT
ma-94	163	12	(	(	PUNCT
ma-94	163	13	2.12	2.12	NUM
ma-94	163	14	)	)	PUNCT
ma-94	163	15	,	,	PUNCT
ma-94	163	16	(	(	PUNCT
ma-94	163	17	2.13	2.13	NUM
ma-94	163	18	)	)	PUNCT
ma-94	163	19	,	,	PUNCT
ma-94	163	20	(	(	PUNCT
ma-94	163	21	2.16	2.16	NUM
ma-94	163	22	)	)	PUNCT
ma-94	163	23	and	and	CCONJ
ma-94	163	24	(	(	PUNCT
ma-94	163	25	2.17	2.17	NUM
ma-94	163	26	)	)	PUNCT
ma-94	163	27	that	that	PRON
ma-94	163	28	h1	h1	VERB
ma-94	163	29	≤	≤	ADJ
ma-94	163	30	f	f	X
ma-94	163	31	(	(	PUNCT
ma-94	163	32	m)⇒	m)⇒	VERB
ma-94	163	33	h	h	NOUN
ma-94	164	1	≤	≤	NUM
ma-94	165	1	f	f	X
ma-94	166	1	(	(	PUNCT
ma-94	166	2	m	m	PROPN
ma-94	166	3	)	)	PUNCT
ma-94	166	4	(	(	PUNCT
ma-94	166	5	2.18	2.18	NUM
ma-94	166	6	)	)	PUNCT
ma-94	166	7	but	but	CCONJ
ma-94	166	8	not	not	PART
ma-94	166	9	necessarily	necessarily	ADV
ma-94	166	10	vice	vice	ADV
ma-94	166	11	versa	versa	ADV
ma-94	166	12	,	,	PUNCT
ma-94	166	13	unless	unless	SCONJ
ma-94	166	14	if	if	SCONJ
ma-94	166	15	h	h	NOUN
ma-94	166	16	=	=	X
ma-94	166	17	h1	h1	PROPN
ma-94	166	18	,	,	PUNCT
ma-94	166	19	vn	vn	PROPN
ma-94	166	20	≤	≤	PROPN
ma-94	166	21	wn	wn	PROPN
ma-94	166	22	,	,	PUNCT
ma-94	166	23	0	0	NUM
ma-94	166	24	≤	≤	NUM
ma-94	166	25	vn+1	vn+1	PROPN
ma-94	167	1	−	−	PROPN
ma-94	167	2	vn	vn	PROPN
ma-94	167	3	≤	≤	PROPN
ma-94	167	4	wn+1	wn+1	VERB
ma-94	167	5	−	−	PROPN
ma-94	167	6	wn	wn	NOUN
ma-94	167	7	and	and	CCONJ
ma-94	167	8	0	0	NUM
ma-94	167	9	≤	≤	NOUN
ma-94	167	10	v∗	v∗	ADJ
ma-94	167	11	≤	≤	PROPN
ma-94	167	12	w∗	w∗	NOUN
ma-94	167	13	=	=	PROPN
ma-94	167	14	lim	lim	PROPN
ma-94	167	15	n−→∞	n−→∞	PROPN
ma-94	167	16	wn	wn	PROPN
ma-94	167	17	.	.	PUNCT
ma-94	168	1	(	(	PUNCT
ma-94	168	2	2	2	X
ma-94	168	3	)	)	PUNCT
ma-94	168	4	in	in	ADP
ma-94	168	5	view	view	NOUN
ma-94	168	6	of	of	ADP
ma-94	168	7	(	(	PUNCT
ma-94	168	8	2.9	2.9	NUM
ma-94	168	9	)	)	PUNCT
ma-94	168	10	and	and	CCONJ
ma-94	168	11	(	(	PUNCT
ma-94	168	12	2.10	2.10	NUM
ma-94	168	13	)	)	PUNCT
ma-94	168	14	sequence	sequence	NOUN
ma-94	168	15	{	{	PUNCT
ma-94	168	16	un	un	PROPN
ma-94	168	17	}	}	PUNCT
ma-94	168	18	defined	define	VERB
ma-94	168	19	for	for	ADP
ma-94	168	20	each	each	DET
ma-94	168	21	n	n	NOUN
ma-94	168	22	=	=	SYM
ma-94	168	23	0	0	NUM
ma-94	168	24	,	,	PUNCT
ma-94	168	25	1	1	NUM
ma-94	168	26	,	,	PUNCT
ma-94	168	27	2	2	NUM
ma-94	168	28	,	,	PUNCT
ma-94	168	29	.	.	PUNCT
ma-94	168	30	.	.	PUNCT
ma-94	168	31	.	.	PUNCT
ma-94	169	1	by	by	ADP
ma-94	169	2	https://doi.org/10.28924/ada/ma.2.18	https://doi.org/10.28924/ada/ma.2.18	PROPN
ma-94	169	3	eur	eur	PROPN
ma-94	169	4	.	.	PUNCT
ma-94	170	1	j.	j.	PROPN
ma-94	170	2	math	math	PROPN
ma-94	170	3	.	.	PUNCT
ma-94	171	1	anal	anal	PROPN
ma-94	171	2	.	.	PUNCT
ma-94	172	1	10.28924	10.28924	NUM
ma-94	172	2	/	/	SYM
ma-94	172	3	ada	ada	PROPN
ma-94	172	4	/	/	SYM
ma-94	172	5	ma.2.18	ma.2.18	PROPN
ma-94	172	6	8	8	NUM
ma-94	172	7	u0	u0	NOUN
ma-94	172	8	=	=	NOUN
ma-94	172	9	0	0	NUM
ma-94	172	10	,	,	PUNCT
ma-94	172	11	u1	u1	NOUN
ma-94	172	12	=	=	SYM
ma-94	172	13	h	h	NOUN
ma-94	172	14	1	1	NUM
ma-94	172	15	p	p	NOUN
ma-94	172	16	1	1	NUM
ma-94	172	17	,	,	PUNCT
ma-94	172	18	u2	u2	NOUN
ma-94	172	19	=	=	PUNCT
ma-94	172	20	u1	u1	PROPN
ma-94	172	21	+	+	CCONJ
ma-94	172	22	h0(u1	h0(u1	NUM
ma-94	172	23	−	−	PROPN
ma-94	172	24	u0)1+p	u0)1+p	NOUN
ma-94	172	25	(	(	PUNCT
ma-94	172	26	1	1	NUM
ma-94	172	27	+	+	NUM
ma-94	172	28	p)(1−h0up1	p)(1−h0up1	NUM
ma-94	172	29	)	)	PUNCT
ma-94	172	30	,	,	PUNCT
ma-94	172	31	un+1	un+1	NOUN
ma-94	172	32	=	=	SYM
ma-94	172	33	un	un	PROPN
ma-94	173	1	+	+	CCONJ
ma-94	173	2	h(un	h(un	PROPN
ma-94	173	3	−	−	PROPN
ma-94	173	4	un−1)1+p	un−1)1+p	PROPN
ma-94	173	5	(	(	PUNCT
ma-94	173	6	1	1	NUM
ma-94	173	7	+	+	NUM
ma-94	173	8	p)(1−h0upn	p)(1−h0upn	NOUN
ma-94	173	9	)	)	PUNCT
ma-94	173	10	is	be	AUX
ma-94	173	11	a	a	DET
ma-94	173	12	tighter	tight	ADJ
ma-94	173	13	majorizing	majorize	VERB
ma-94	173	14	sequence	sequence	NOUN
ma-94	173	15	than	than	ADP
ma-94	173	16	{	{	PUNCT
ma-94	173	17	vn	vn	NOUN
ma-94	173	18	}	}	PUNCT
ma-94	173	19	and	and	CCONJ
ma-94	173	20	can	can	AUX
ma-94	173	21	replace	replace	VERB
ma-94	173	22	it	it	PRON
ma-94	173	23	in	in	ADP
ma-94	173	24	theorem	theorem	ADJ
ma-94	173	25	2.11	2.11	NUM
ma-94	173	26	and	and	CCONJ
ma-94	173	27	theorem	theorem	VERB
ma-94	173	28	2.12	2.12	NUM
ma-94	173	29	.	.	PUNCT
ma-94	174	1	concerning	concern	VERB
ma-94	174	2	the	the	DET
ma-94	174	3	uniqueness	uniqueness	NOUN
ma-94	174	4	of	of	ADP
ma-94	174	5	the	the	DET
ma-94	174	6	solution	solution	NOUN
ma-94	174	7	x∗	x∗	X
ma-94	174	8	we	we	PRON
ma-94	174	9	provide	provide	VERB
ma-94	174	10	a	a	DET
ma-94	174	11	result	result	NOUN
ma-94	174	12	based	base	VERB
ma-94	174	13	only	only	ADV
ma-94	174	14	on	on	ADP
ma-94	174	15	(	(	PUNCT
ma-94	174	16	2.1	2.1	NUM
ma-94	174	17	)	)	PUNCT
ma-94	174	18	.	.	PUNCT
ma-94	175	1	proposition	proposition	NOUN
ma-94	175	2	2.14	2.14	NUM
ma-94	175	3	.	.	PUNCT
ma-94	176	1	suppose	suppose	VERB
ma-94	176	2	:	:	PUNCT
ma-94	176	3	(	(	PUNCT
ma-94	176	4	1	1	X
ma-94	176	5	)	)	PUNCT
ma-94	176	6	the	the	DET
ma-94	176	7	point	point	NOUN
ma-94	176	8	x∗	x∗	PROPN
ma-94	176	9	∈	∈	PROPN
ma-94	176	10	u(x0	u(x0	NOUN
ma-94	176	11	,	,	PUNCT
ma-94	176	12	a	a	PRON
ma-94	176	13	)	)	PUNCT
ma-94	177	1	⊂	⊂	PROPN
ma-94	177	2	ω	ω	PROPN
ma-94	177	3	is	be	AUX
ma-94	177	4	a	a	DET
ma-94	177	5	simple	simple	ADJ
ma-94	177	6	solution	solution	NOUN
ma-94	177	7	of	of	ADP
ma-94	177	8	equation	equation	NOUN
ma-94	177	9	f	f	X
ma-94	177	10	(	(	PUNCT
ma-94	177	11	x	x	X
ma-94	177	12	)	)	PUNCT
ma-94	177	13	=	=	SYM
ma-94	177	14	0	0	NUM
ma-94	177	15	for	for	ADP
ma-94	177	16	some	some	DET
ma-94	177	17	a	a	DET
ma-94	177	18	>	>	X
ma-94	177	19	0	0	NUM
ma-94	177	20	.	.	PUNCT
ma-94	178	1	(	(	PUNCT
ma-94	178	2	2	2	X
ma-94	178	3	)	)	PUNCT
ma-94	178	4	condition	condition	NOUN
ma-94	178	5	(	(	PUNCT
ma-94	178	6	2.1	2.1	NUM
ma-94	178	7	)	)	PUNCT
ma-94	178	8	holds	hold	VERB
ma-94	178	9	.	.	PUNCT
ma-94	179	1	(	(	PUNCT
ma-94	179	2	3	3	X
ma-94	179	3	)	)	PUNCT
ma-94	179	4	there	there	PRON
ma-94	179	5	exist	exist	VERB
ma-94	179	6	b	b	NUM
ma-94	179	7	≥	≥	NOUN
ma-94	179	8	a	a	DET
ma-94	179	9	such	such	ADJ
ma-94	179	10	that	that	DET
ma-94	179	11	h0	h0	PROPN
ma-94	179	12	∫	∫	PROPN
ma-94	179	13	1	1	NUM
ma-94	179	14	0	0	NUM
ma-94	179	15	(	(	PUNCT
ma-94	179	16	(	(	PUNCT
ma-94	179	17	1−	1−	NUM
ma-94	179	18	τ)a	τ)a	X
ma-94	179	19	+	+	NUM
ma-94	179	20	τb)pdτ	τb)pdτ	NOUN
ma-94	179	21	<	<	X
ma-94	179	22	1	1	NUM
ma-94	179	23	.	.	PUNCT
ma-94	180	1	(	(	PUNCT
ma-94	180	2	2.19	2.19	NUM
ma-94	180	3	)	)	PUNCT
ma-94	180	4	let	let	VERB
ma-94	180	5	g	g	NOUN
ma-94	180	6	=	=	PUNCT
ma-94	180	7	u[x0	u[x0	NOUN
ma-94	180	8	,	,	PUNCT
ma-94	180	9	b	b	X
ma-94	180	10	]	]	X
ma-94	180	11	∩ω	∩ω	INTJ
ma-94	180	12	.	.	PUNCT
ma-94	181	1	then	then	ADV
ma-94	181	2	,	,	PUNCT
ma-94	181	3	the	the	DET
ma-94	181	4	point	point	NOUN
ma-94	181	5	x∗	x∗	PROPN
ma-94	181	6	is	be	AUX
ma-94	181	7	the	the	DET
ma-94	181	8	only	only	ADJ
ma-94	181	9	solution	solution	NOUN
ma-94	181	10	of	of	ADP
ma-94	181	11	equation	equation	NOUN
ma-94	181	12	f	f	X
ma-94	181	13	(	(	PUNCT
ma-94	181	14	x	x	X
ma-94	181	15	)	)	PUNCT
ma-94	181	16	=	=	SYM
ma-94	181	17	0	0	NUM
ma-94	181	18	in	in	ADP
ma-94	181	19	the	the	DET
ma-94	181	20	set	set	NOUN
ma-94	181	21	g.	g.	NOUN
ma-94	181	22	proof	proof	NOUN
ma-94	181	23	.	.	PUNCT
ma-94	182	1	let	let	VERB
ma-94	182	2	z∗	z∗	PROPN
ma-94	182	3	∈	∈	PROPN
ma-94	182	4	g	g	NOUN
ma-94	182	5	with	with	ADP
ma-94	182	6	f	f	PROPN
ma-94	182	7	(	(	PUNCT
ma-94	182	8	z∗	z∗	PROPN
ma-94	182	9	)	)	PUNCT
ma-94	182	10	=	=	SYM
ma-94	183	1	0	0	X
ma-94	183	2	.	.	PUNCT
ma-94	183	3	by	by	ADP
ma-94	183	4	(	(	PUNCT
ma-94	183	5	2.1	2.1	NUM
ma-94	183	6	)	)	PUNCT
ma-94	183	7	and	and	CCONJ
ma-94	183	8	(	(	PUNCT
ma-94	183	9	2.19	2.19	NUM
ma-94	183	10	)	)	PUNCT
ma-94	183	11	,	,	PUNCT
ma-94	183	12	we	we	PRON
ma-94	183	13	obtain	obtain	VERB
ma-94	183	14	in	in	ADP
ma-94	183	15	turn	turn	NOUN
ma-94	183	16	for	for	ADP
ma-94	183	17	q	q	NOUN
ma-94	183	18	=	=	SYM
ma-94	183	19	∫	∫	PROPN
ma-94	183	20	1	1	NUM
ma-94	183	21	0	0	NUM
ma-94	183	22	f	f	PROPN
ma-94	183	23	′(x∗	′(x∗	NOUN
ma-94	183	24	+	+	CCONJ
ma-94	183	25	τ(z∗	τ(z∗	ADJ
ma-94	183	26	−	−	NOUN
ma-94	183	27	x∗))dτ	x∗))dτ	PROPN
ma-94	184	1	‖f	‖f	ADP
ma-94	184	2	′(x0)−1(q−	′(x0)−1(q−	PROPN
ma-94	184	3	f	f	NOUN
ma-94	184	4	′(x0))‖	′(x0))‖	NUM
ma-94	184	5	≤	≤	PROPN
ma-94	184	6	h0	h0	PROPN
ma-94	184	7	∫	∫	PROPN
ma-94	184	8	1	1	NUM
ma-94	184	9	0	0	NUM
ma-94	184	10	‖x∗	‖x∗	PUNCT
ma-94	185	1	+	+	CCONJ
ma-94	185	2	τ(z∗	τ(z∗	ADV
ma-94	185	3	−	−	NOUN
ma-94	185	4	x∗)−	x∗)−	PRON
ma-94	185	5	x0‖pdτ	x0‖pdτ	PROPN
ma-94	185	6	≤	≤	PROPN
ma-94	185	7	h0	h0	PROPN
ma-94	185	8	∫	∫	PROPN
ma-94	185	9	1	1	NUM
ma-94	185	10	0	0	NUM
ma-94	186	1	[	[	X
ma-94	186	2	(	(	PUNCT
ma-94	186	3	1−	1−	NUM
ma-94	186	4	τ)‖x∗	τ)‖x∗	NUM
ma-94	186	5	−	−	PROPN
ma-94	186	6	x0‖+	x0‖+	SYM
ma-94	186	7	τ‖z∗	τ‖z∗	PROPN
ma-94	186	8	−	−	PROPN
ma-94	186	9	x0‖]pdτ	x0‖]pdτ	PROPN
ma-94	186	10	≤	≤	PROPN
ma-94	186	11	h0	h0	NOUN
ma-94	186	12	∫	∫	PROPN
ma-94	186	13	1	1	NUM
ma-94	186	14	0	0	NUM
ma-94	186	15	(	(	PUNCT
ma-94	186	16	(	(	PUNCT
ma-94	186	17	1−	1−	NUM
ma-94	186	18	τ)a	τ)a	X
ma-94	186	19	+	+	CCONJ
ma-94	186	20	τb)pdτ	τb)pdτ	NOUN
ma-94	186	21	<	<	X
ma-94	186	22	1	1	NUM
ma-94	186	23	,	,	PUNCT
ma-94	186	24	showing	show	VERB
ma-94	186	25	z∗	z∗	NOUN
ma-94	186	26	=	=	PUNCT
ma-94	186	27	x∗	x∗	PROPN
ma-94	186	28	by	by	ADP
ma-94	186	29	the	the	DET
ma-94	186	30	invertibility	invertibility	NOUN
ma-94	186	31	of	of	ADP
ma-94	186	32	q	q	NOUN
ma-94	186	33	and	and	CCONJ
ma-94	186	34	the	the	DET
ma-94	186	35	approximation	approximation	NOUN
ma-94	186	36	q(x∗−	q(x∗−	PROPN
ma-94	186	37	z∗	z∗	PROPN
ma-94	186	38	)	)	PUNCT
ma-94	187	1	=	=	SYM
ma-94	187	2	f	f	PROPN
ma-94	187	3	(	(	PUNCT
ma-94	187	4	x∗)−f	x∗)−f	PROPN
ma-94	187	5	(	(	PUNCT
ma-94	187	6	z∗	z∗	NOUN
ma-94	187	7	)	)	PUNCT
ma-94	187	8	=	=	SYM
ma-94	187	9	0	0	X
ma-94	187	10	.	.	PUNCT
ma-94	187	11	�	�	PROPN
ma-94	187	12	notice	notice	VERB
ma-94	187	13	that	that	SCONJ
ma-94	187	14	if	if	SCONJ
ma-94	187	15	k	k	PROPN
ma-94	187	16	=	=	PRON
ma-94	187	17	h1	h1	VERB
ma-94	187	18	the	the	DET
ma-94	187	19	results	result	NOUN
ma-94	187	20	coincide	coincide	VERB
ma-94	187	21	to	to	ADP
ma-94	187	22	the	the	DET
ma-94	187	23	ones	one	NOUN
ma-94	187	24	of	of	ADP
ma-94	187	25	theorem	theorem	NOUN
ma-94	187	26	3.4	3.4	NUM
ma-94	187	27	in	in	ADP
ma-94	187	28	[	[	X
ma-94	187	29	9	9	NUM
ma-94	187	30	]	]	PUNCT
ma-94	187	31	.	.	PUNCT
ma-94	188	1	but	but	CCONJ
ma-94	188	2	,	,	PUNCT
ma-94	188	3	if	if	SCONJ
ma-94	188	4	k	k	PROPN
ma-94	188	5	<	<	X
ma-94	188	6	h1then	h1then	ADV
ma-94	188	7	they	they	PRON
ma-94	188	8	constitute	constitute	VERB
ma-94	188	9	an	an	DET
ma-94	188	10	extension	extension	NOUN
ma-94	188	11	.	.	PUNCT
ma-94	189	1	remark	remark	PROPN
ma-94	189	2	2.15	2.15	NUM
ma-94	189	3	.	.	PUNCT
ma-94	190	1	(	(	PUNCT
ma-94	190	2	a	a	X
ma-94	190	3	)	)	PUNCT
ma-94	190	4	we	we	PRON
ma-94	190	5	gave	give	VERB
ma-94	190	6	the	the	DET
ma-94	190	7	results	result	NOUN
ma-94	190	8	in	in	ADP
ma-94	190	9	affine	affine	ADJ
ma-94	190	10	invariant	invariant	ADJ
ma-94	190	11	form	form	NOUN
ma-94	190	12	.	.	PUNCT
ma-94	191	1	(	(	PUNCT
ma-94	191	2	b)the	b)the	DET
ma-94	191	3	results	result	NOUN
ma-94	191	4	in	in	ADP
ma-94	191	5	this	this	DET
ma-94	191	6	study	study	NOUN
ma-94	191	7	can	can	AUX
ma-94	191	8	be	be	AUX
ma-94	191	9	extended	extend	VERB
ma-94	191	10	more	more	ADJ
ma-94	191	11	if	if	SCONJ
ma-94	191	12	we	we	PRON
ma-94	191	13	consider	consider	VERB
ma-94	191	14	the	the	DET
ma-94	191	15	set	set	NOUN
ma-94	191	16	s	s	PART
ma-94	191	17	=	=	SYM
ma-94	191	18	u(x1	u(x1	ADJ
ma-94	191	19	,	,	PUNCT
ma-94	191	20	1	1	NUM
ma-94	191	21	h1	h1	NOUN
ma-94	191	22	/	/	SYM
ma-94	191	23	p	p	NOUN
ma-94	191	24	−	−	PROPN
ma-94	191	25	d	d	NOUN
ma-94	191	26	)	)	PUNCT
ma-94	191	27	provided	provide	VERB
ma-94	191	28	that	that	SCONJ
ma-94	191	29	h1	h1	PROPN
ma-94	191	30	/	/	SYM
ma-94	191	31	pd	pd	X
ma-94	191	32	<	<	X
ma-94	191	33	1	1	NUM
ma-94	191	34	.	.	PUNCT
ma-94	192	1	moreover	moreover	ADV
ma-94	192	2	,	,	PUNCT
ma-94	192	3	suppose	suppose	VERB
ma-94	192	4	s	s	PROPN
ma-94	192	5	⊂	⊂	PROPN
ma-94	192	6	ω	ω	PROPN
ma-94	192	7	.	.	PUNCT
ma-94	193	1	then	then	ADV
ma-94	193	2	,	,	PUNCT
ma-94	193	3	s	s	PROPN
ma-94	193	4	⊂	⊂	PROPN
ma-94	193	5	ω0	ω0	NOUN
ma-94	193	6	,	,	PUNCT
ma-94	193	7	so	so	SCONJ
ma-94	193	8	the	the	DET
ma-94	193	9	hölderian	hölderian	ADJ
ma-94	193	10	constant	constant	ADJ
ma-94	193	11	corresponding	corresponding	NOUN
ma-94	193	12	to	to	ADP
ma-94	193	13	s	s	PRON
ma-94	193	14	is	be	AUX
ma-94	193	15	at	at	ADV
ma-94	193	16	least	least	ADJ
ma-94	193	17	as	as	ADV
ma-94	193	18	small	small	ADJ
ma-94	193	19	as	as	ADP
ma-94	193	20	k	k	PROPN
ma-94	193	21	,	,	PUNCT
ma-94	193	22	and	and	CCONJ
ma-94	193	23	can	can	AUX
ma-94	193	24	replace	replace	VERB
ma-94	193	25	it	it	PRON
ma-94	193	26	in	in	ADP
ma-94	193	27	all	all	DET
ma-94	193	28	previous	previous	ADJ
ma-94	193	29	results	result	NOUN
ma-94	193	30	.	.	PUNCT
ma-94	194	1	references	reference	NOUN
ma-94	194	2	[	[	X
ma-94	194	3	1	1	X
ma-94	194	4	]	]	PUNCT
ma-94	194	5	j.	j.	PROPN
ma-94	194	6	appell	appell	PROPN
ma-94	194	7	,	,	PUNCT
ma-94	194	8	e.d	e.d	PROPN
ma-94	194	9	.	.	PROPN
ma-94	194	10	pascale	pascale	PROPN
ma-94	194	11	,	,	PUNCT
ma-94	194	12	j.v	j.v	PROPN
ma-94	194	13	.	.	PROPN
ma-94	195	1	lysenko	lysenko	PROPN
ma-94	195	2	,	,	PUNCT
ma-94	195	3	p.p	p.p	PROPN
ma-94	195	4	.	.	PROPN
ma-94	195	5	zabrejko	zabrejko	PROPN
ma-94	195	6	,	,	PUNCT
ma-94	195	7	new	new	ADJ
ma-94	195	8	results	result	NOUN
ma-94	195	9	on	on	ADP
ma-94	195	10	newton	newton	PROPN
ma-94	195	11	-	-	PUNCT
ma-94	195	12	kantorovich	kantorovich	PROPN
ma-94	195	13	approximations	approximation	NOUN
ma-94	195	14	with	with	ADP
ma-94	195	15	appli	appli	PROPN
ma-94	195	16	-	-	PUNCT
ma-94	195	17	cations	cation	NOUN
ma-94	195	18	to	to	PART
ma-94	195	19	nonlinear	nonlinear	VERB
ma-94	195	20	integral	integral	ADJ
ma-94	195	21	equations	equation	NOUN
ma-94	195	22	,	,	PUNCT
ma-94	195	23	numer	numer	PROPN
ma-94	195	24	.	.	PUNCT
ma-94	196	1	funct	funct	PROPN
ma-94	196	2	.	.	PUNCT
ma-94	197	1	anal	anal	PROPN
ma-94	197	2	.	.	PUNCT
ma-94	198	1	optim	optim	PROPN
ma-94	198	2	.	.	PUNCT
ma-94	199	1	18	18	NUM
ma-94	199	2	(	(	PUNCT
ma-94	199	3	1997	1997	NUM
ma-94	199	4	)	)	PUNCT
ma-94	199	5	1–17	1–17	NOUN
ma-94	199	6	.	.	PUNCT
ma-94	200	1	https://doi.org/10.1080/	https://doi.org/10.1080/	NOUN
ma-94	200	2	01630569708816744	01630569708816744	NUM
ma-94	200	3	.	.	PUNCT
ma-94	201	1	https://doi.org/10.28924/ada/ma.2.18	https://doi.org/10.28924/ada/ma.2.18	PROPN
ma-94	201	2	https://doi.org/10.1080/01630569708816744	https://doi.org/10.1080/01630569708816744	X
ma-94	201	3	https://doi.org/10.1080/01630569708816744	https://doi.org/10.1080/01630569708816744	ADJ
ma-94	201	4	eur	eur	NOUN
ma-94	201	5	.	.	PUNCT
ma-94	202	1	j.	j.	PROPN
ma-94	202	2	math	math	PROPN
ma-94	202	3	.	.	PUNCT
ma-94	203	1	anal	anal	PROPN
ma-94	203	2	.	.	PUNCT
ma-94	204	1	10.28924	10.28924	NUM
ma-94	204	2	/	/	SYM
ma-94	204	3	ada	ada	PROPN
ma-94	204	4	/	/	SYM
ma-94	204	5	ma.2.18	ma.2.18	PROPN
ma-94	204	6	9	9	NUM
ma-94	204	7	[	[	X
ma-94	204	8	2	2	NUM
ma-94	204	9	]	]	X
ma-94	204	10	i.k	i.k	PROPN
ma-94	204	11	.	.	PROPN
ma-94	204	12	argyros	argyros	PROPN
ma-94	204	13	,	,	PUNCT
ma-94	204	14	s.	s.	PROPN
ma-94	204	15	hilout	hilout	PROPN
ma-94	204	16	,	,	PUNCT
ma-94	204	17	inexact	inexact	ADJ
ma-94	204	18	newton	newton	PROPN
ma-94	204	19	-	-	PUNCT
ma-94	204	20	type	type	NOUN
ma-94	204	21	methods	method	NOUN
ma-94	204	22	,	,	PUNCT
ma-94	204	23	j.	j.	PROPN
ma-94	204	24	complex	complex	PROPN
ma-94	204	25	.	.	PUNCT
ma-94	205	1	26	26	NUM
ma-94	205	2	(	(	PUNCT
ma-94	205	3	2010	2010	NUM
ma-94	205	4	)	)	PUNCT
ma-94	206	1	577–590	577–590	NUM
ma-94	206	2	.	.	PUNCT
ma-94	207	1	https://doi.org/10.1016/	https://doi.org/10.1016/	PROPN
ma-94	207	2	j.jco.2010.08.006.[3	j.jco.2010.08.006.[3	NOUN
ma-94	207	3	]	]	X
ma-94	207	4	i.k	i.k	PROPN
ma-94	207	5	.	.	PROPN
ma-94	207	6	argyros	argyros	PROPN
ma-94	207	7	,	,	PUNCT
ma-94	207	8	convergence	convergence	NOUN
ma-94	207	9	and	and	CCONJ
ma-94	207	10	applications	application	NOUN
ma-94	207	11	of	of	ADP
ma-94	207	12	newton	newton	NOUN
ma-94	207	13	-	-	PUNCT
ma-94	207	14	type	type	NOUN
ma-94	207	15	iterations	iteration	NOUN
ma-94	207	16	,	,	PUNCT
ma-94	207	17	springer	springer	NOUN
ma-94	207	18	new	new	PROPN
ma-94	207	19	york	york	PROPN
ma-94	207	20	,	,	PUNCT
ma-94	207	21	2008	2008	NUM
ma-94	207	22	.	.	PUNCT
ma-94	208	1	https://doi	https://doi	PROPN
ma-94	208	2	.	.	PUNCT
ma-94	208	3	org/10.1007/978	org/10.1007/978	PROPN
ma-94	208	4	-	-	PUNCT
ma-94	208	5	0	0	NUM
ma-94	208	6	-	-	PUNCT
ma-94	208	7	387	387	NUM
ma-94	208	8	-	-	PUNCT
ma-94	208	9	72743	72743	NUM
ma-94	208	10	-	-	SYM
ma-94	208	11	1.[4	1.[4	PROPN
ma-94	208	12	]	]	X
ma-94	208	13	i.k	i.k	PROPN
ma-94	208	14	.	.	PROPN
ma-94	208	15	argyros	argyros	PROPN
ma-94	208	16	,	,	PUNCT
ma-94	208	17	s.	s.	PROPN
ma-94	208	18	george	george	PROPN
ma-94	208	19	,	,	PUNCT
ma-94	208	20	mathematical	mathematical	ADJ
ma-94	208	21	modeling	modeling	NOUN
ma-94	208	22	for	for	ADP
ma-94	208	23	the	the	DET
ma-94	208	24	solution	solution	NOUN
ma-94	208	25	of	of	ADP
ma-94	208	26	equations	equation	NOUN
ma-94	208	27	and	and	CCONJ
ma-94	208	28	systems	system	NOUN
ma-94	208	29	of	of	ADP
ma-94	208	30	equations	equation	NOUN
ma-94	208	31	with	with	ADP
ma-94	208	32	appli	appli	PROPN
ma-94	208	33	-	-	PUNCT
ma-94	208	34	cations	cation	NOUN
ma-94	208	35	,	,	PUNCT
ma-94	208	36	volume	volume	NOUN
ma-94	208	37	-	-	PUNCT
ma-94	208	38	iv	iv	NOUN
ma-94	208	39	,	,	PUNCT
ma-94	208	40	nova	nova	PROPN
ma-94	208	41	publisher	publisher	NOUN
ma-94	208	42	,	,	PUNCT
ma-94	208	43	ny	ny	PROPN
ma-94	208	44	,	,	PUNCT
ma-94	208	45	2021.[5	2021.[5	NUM
ma-94	208	46	]	]	X
ma-94	208	47	f.	f.	PROPN
ma-94	208	48	cianciaruso	cianciaruso	PROPN
ma-94	208	49	,	,	PUNCT
ma-94	208	50	e.	e.	PROPN
ma-94	208	51	de	de	PROPN
ma-94	208	52	pascale	pascale	PROPN
ma-94	208	53	,	,	PUNCT
ma-94	208	54	newton	newton	PROPN
ma-94	208	55	–	–	PUNCT
ma-94	208	56	kantorovich	kantorovich	PROPN
ma-94	208	57	approximations	approximation	NOUN
ma-94	208	58	when	when	SCONJ
ma-94	208	59	the	the	DET
ma-94	208	60	derivative	derivative	NOUN
ma-94	208	61	is	be	AUX
ma-94	208	62	hölderian	hölderian	ADJ
ma-94	208	63	:	:	PUNCT
ma-94	208	64	old	old	ADJ
ma-94	208	65	and	and	CCONJ
ma-94	208	66	newresults	newresult	NOUN
ma-94	208	67	,	,	PUNCT
ma-94	208	68	numer	numer	PROPN
ma-94	208	69	.	.	PUNCT
ma-94	209	1	funct	funct	PROPN
ma-94	209	2	.	.	PUNCT
ma-94	210	1	anal	anal	PROPN
ma-94	210	2	.	.	PUNCT
ma-94	211	1	optim	optim	PROPN
ma-94	211	2	.	.	PUNCT
ma-94	212	1	24	24	NUM
ma-94	212	2	(	(	PUNCT
ma-94	212	3	2003	2003	NUM
ma-94	212	4	)	)	PUNCT
ma-94	213	1	713–723	713–723	NUM
ma-94	213	2	.	.	PUNCT
ma-94	214	1	https://doi.org/10.1081/nfa-120026367.[6	https://doi.org/10.1081/nfa-120026367.[6	PRON
ma-94	214	2	]	]	PUNCT
ma-94	214	3	f.	f.	PROPN
ma-94	214	4	cianciaruso	cianciaruso	PROPN
ma-94	214	5	,	,	PUNCT
ma-94	214	6	e.	e.	PROPN
ma-94	214	7	de	de	PROPN
ma-94	214	8	pascale	pascale	PROPN
ma-94	214	9	,	,	PUNCT
ma-94	214	10	estimates	estimate	NOUN
ma-94	214	11	of	of	ADP
ma-94	214	12	majorizing	majorize	VERB
ma-94	214	13	sequences	sequence	NOUN
ma-94	214	14	in	in	ADP
ma-94	214	15	the	the	DET
ma-94	214	16	newton	newton	PROPN
ma-94	214	17	–	–	PUNCT
ma-94	214	18	kantorovich	kantorovich	PROPN
ma-94	214	19	method	method	NOUN
ma-94	214	20	:	:	PUNCT
ma-94	214	21	a	a	DET
ma-94	214	22	furtherimprovement	furtherimprovement	NOUN
ma-94	214	23	,	,	PUNCT
ma-94	214	24	j.	j.	PROPN
ma-94	214	25	math	math	PROPN
ma-94	214	26	.	.	PUNCT
ma-94	215	1	anal	anal	PROPN
ma-94	215	2	.	.	PUNCT
ma-94	215	3	appl	appl	PROPN
ma-94	215	4	.	.	PUNCT
ma-94	216	1	322	322	NUM
ma-94	216	2	(	(	PUNCT
ma-94	216	3	2006	2006	NUM
ma-94	216	4	)	)	PUNCT
ma-94	217	1	329–335	329–335	NUM
ma-94	217	2	.	.	PUNCT
ma-94	218	1	https://doi.org/10.1016/j.jmaa.2005.09.008.[7	https://doi.org/10.1016/j.jmaa.2005.09.008.[7	PROPN
ma-94	218	2	]	]	X
ma-94	218	3	n.t	n.t	PROPN
ma-94	218	4	.	.	PROPN
ma-94	218	5	demidovich	demidovich	PROPN
ma-94	218	6	,	,	PUNCT
ma-94	218	7	p.p	p.p	PROPN
ma-94	218	8	.	.	PROPN
ma-94	218	9	zabreiko	zabreiko	PROPN
ma-94	218	10	,	,	PUNCT
ma-94	218	11	j.v	j.v	PROPN
ma-94	218	12	.	.	PROPN
ma-94	218	13	lysenko	lysenko	PROPN
ma-94	218	14	,	,	PUNCT
ma-94	218	15	some	some	DET
ma-94	218	16	remarks	remark	NOUN
ma-94	218	17	on	on	ADP
ma-94	218	18	the	the	DET
ma-94	218	19	newtonkantorovich	newtonkantorovich	NOUN
ma-94	218	20	method	method	NOUN
ma-94	218	21	for	for	ADP
ma-94	218	22	nonlinear	nonlinear	ADJ
ma-94	218	23	equa	equa	NOUN
ma-94	218	24	-	-	PUNCT
ma-94	218	25	tions	tion	NOUN
ma-94	218	26	with	with	ADP
ma-94	218	27	hölder	hölder	PROPN
ma-94	218	28	continuous	continuous	ADJ
ma-94	218	29	linearizations	linearization	NOUN
ma-94	218	30	,	,	PUNCT
ma-94	218	31	izv	izv	PROPN
ma-94	218	32	.	.	PROPN
ma-94	218	33	akad	akad	PROPN
ma-94	218	34	.	.	PUNCT
ma-94	219	1	nauk	nauk	PROPN
ma-94	219	2	,	,	PUNCT
ma-94	219	3	beloruss	beloruss	ADJ
ma-94	219	4	,	,	PUNCT
ma-94	219	5	3	3	NUM
ma-94	219	6	(	(	PUNCT
ma-94	219	7	1993	1993	NUM
ma-94	219	8	)	)	PUNCT
ma-94	219	9	22	22	NUM
ma-94	219	10	-	-	SYM
ma-94	219	11	26	26	NUM
ma-94	219	12	(	(	PUNCT
ma-94	219	13	russian).[8	russian).[8	NOUN
ma-94	219	14	]	]	PUNCT
ma-94	219	15	e.	e.	PROPN
ma-94	219	16	de	de	PROPN
ma-94	219	17	pascale	pascale	PROPN
ma-94	219	18	,	,	PUNCT
ma-94	219	19	p.p	p.p	PROPN
ma-94	219	20	.	.	PROPN
ma-94	219	21	zabrejko	zabrejko	PROPN
ma-94	219	22	,	,	PUNCT
ma-94	219	23	convergence	convergence	NOUN
ma-94	219	24	of	of	ADP
ma-94	219	25	the	the	DET
ma-94	219	26	newton	newton	PROPN
ma-94	219	27	-	-	PUNCT
ma-94	219	28	kantorovich	kantorovich	PROPN
ma-94	219	29	method	method	NOUN
ma-94	219	30	under	under	ADP
ma-94	219	31	vertgeim	vertgeim	NOUN
ma-94	219	32	conditions	condition	NOUN
ma-94	219	33	:	:	PUNCT
ma-94	219	34	a	a	DET
ma-94	219	35	newimprovement	newimprovement	NOUN
ma-94	219	36	,	,	PUNCT
ma-94	219	37	z.	z.	PROPN
ma-94	219	38	anal	anal	PROPN
ma-94	219	39	.	.	PUNCT
ma-94	220	1	anwend	anwend	PROPN
ma-94	220	2	.	.	PUNCT
ma-94	221	1	17	17	NUM
ma-94	221	2	(	(	PUNCT
ma-94	221	3	1998	1998	NUM
ma-94	221	4	)	)	PUNCT
ma-94	222	1	271–280	271–280	NUM
ma-94	222	2	.	.	PUNCT
ma-94	222	3	https://doi.org/10.4171/zaa/821.[9	https://doi.org/10.4171/zaa/821.[9	NOUN
ma-94	222	4	]	]	PUNCT
ma-94	222	5	j.	j.	PROPN
ma-94	222	6	a.	a.	PROPN
ma-94	222	7	ezquerro	ezquerro	PROPN
ma-94	222	8	,	,	PUNCT
ma-94	222	9	m.	m.	PROPN
ma-94	222	10	hernandez	hernandez	PROPN
ma-94	222	11	-	-	PUNCT
ma-94	222	12	veron	veron	PROPN
ma-94	222	13	,	,	PUNCT
ma-94	222	14	mild	mild	ADJ
ma-94	222	15	differentiability	differentiability	NOUN
ma-94	222	16	conditions	condition	NOUN
ma-94	222	17	for	for	ADP
ma-94	222	18	newton	newton	PROPN
ma-94	222	19	’s	’s	PART
ma-94	222	20	method	method	NOUN
ma-94	222	21	in	in	ADP
ma-94	222	22	banach	banach	NOUN
ma-94	222	23	spaces	space	NOUN
ma-94	222	24	,	,	PUNCT
ma-94	222	25	fron	fron	NOUN
ma-94	222	26	-	-	PUNCT
ma-94	222	27	tiers	tier	NOUN
ma-94	222	28	in	in	ADP
ma-94	222	29	mathematics	mathematic	NOUN
ma-94	222	30	,	,	PUNCT
ma-94	222	31	birkhauser	birkhauser	NOUN
ma-94	222	32	cham	cham	PROPN
ma-94	222	33	,	,	PUNCT
ma-94	222	34	switzerland	switzerland	PROPN
ma-94	222	35	,	,	PUNCT
ma-94	222	36	(	(	PUNCT
ma-94	222	37	2020	2020	NUM
ma-94	222	38	)	)	PUNCT
ma-94	222	39	,	,	PUNCT
ma-94	222	40	https://doi.org/10.1007/978-3-030-48702-7.[10	https://doi.org/10.1007/978-3-030-48702-7.[10	X
ma-94	222	41	]	]	X
ma-94	222	42	l.v	l.v	PROPN
ma-94	222	43	.	.	PROPN
ma-94	222	44	kantorovich	kantorovich	PROPN
ma-94	222	45	,	,	PUNCT
ma-94	222	46	g.p	g.p	PROPN
ma-94	222	47	.	.	PROPN
ma-94	222	48	akilov	akilov	PROPN
ma-94	222	49	,	,	PUNCT
ma-94	222	50	functional	functional	ADJ
ma-94	222	51	analysis	analysis	NOUN
ma-94	222	52	in	in	ADP
ma-94	222	53	normed	normed	ADJ
ma-94	222	54	spaces	space	NOUN
ma-94	222	55	,	,	PUNCT
ma-94	222	56	the	the	DET
ma-94	222	57	macmillan	macmillan	PROPN
ma-94	222	58	co	co	PROPN
ma-94	222	59	,	,	PUNCT
ma-94	222	60	new	new	PROPN
ma-94	222	61	york	york	PROPN
ma-94	222	62	,	,	PUNCT
ma-94	222	63	(	(	PUNCT
ma-94	222	64	1964).[11	1964).[11	NUM
ma-94	222	65	]	]	X
ma-94	222	66	h.b	h.b	PROPN
ma-94	222	67	.	.	PROPN
ma-94	222	68	keller	keller	PROPN
ma-94	222	69	,	,	PUNCT
ma-94	222	70	newton	newton	PROPN
ma-94	222	71	’s	’s	PART
ma-94	222	72	method	method	NOUN
ma-94	222	73	under	under	ADP
ma-94	222	74	mild	mild	ADJ
ma-94	222	75	differentiability	differentiability	NOUN
ma-94	222	76	conditions	condition	NOUN
ma-94	222	77	,	,	PUNCT
ma-94	222	78	j.	j.	PROPN
ma-94	222	79	computer	computer	PROPN
ma-94	222	80	syst	syst	PROPN
ma-94	222	81	.	.	PUNCT
ma-94	223	1	sci	sci	PROPN
ma-94	223	2	.	.	PROPN
ma-94	223	3	4	4	NUM
ma-94	223	4	(	(	PUNCT
ma-94	223	5	1970	1970	NUM
ma-94	223	6	)	)	PUNCT
ma-94	224	1	15–28	15–28	PROPN
ma-94	224	2	.	.	PUNCT
ma-94	225	1	https	https	NOUN
ma-94	225	2	:	:	PUNCT
ma-94	225	3	//doi.org/10.1016	//doi.org/10.1016	PROPN
ma-94	225	4	/	/	SYM
ma-94	225	5	s0022	s0022	NOUN
ma-94	225	6	-	-	PUNCT
ma-94	225	7	0000(70)80009	0000(70)80009	NUM
ma-94	225	8	-	-	SYM
ma-94	225	9	5.[12	5.[12	NUM
ma-94	225	10	]	]	X
ma-94	225	11	j.v	j.v	PROPN
ma-94	225	12	.	.	PROPN
ma-94	226	1	lysenko	lysenko	PROPN
ma-94	226	2	,	,	PUNCT
ma-94	226	3	conditions	condition	NOUN
ma-94	226	4	for	for	ADP
ma-94	226	5	the	the	DET
ma-94	226	6	convergence	convergence	NOUN
ma-94	226	7	of	of	ADP
ma-94	226	8	the	the	DET
ma-94	226	9	newton	newton	PROPN
ma-94	226	10	-	-	PUNCT
ma-94	226	11	kantorovich	kantorovich	PROPN
ma-94	226	12	method	method	NOUN
ma-94	226	13	for	for	ADP
ma-94	226	14	nonlinear	nonlinear	ADJ
ma-94	226	15	equations	equation	NOUN
ma-94	226	16	with	with	ADP
ma-94	226	17	hölderlinearization	hölderlinearization	NOUN
ma-94	226	18	,	,	PUNCT
ma-94	226	19	dokl	dokl	NOUN
ma-94	226	20	.	.	PUNCT
ma-94	227	1	akad	akad	PROPN
ma-94	227	2	.	.	PUNCT
ma-94	228	1	nauk	nauk	PROPN
ma-94	228	2	.	.	PROPN
ma-94	228	3	bssr	bssr	PROPN
ma-94	228	4	,	,	PUNCT
ma-94	228	5	38	38	NUM
ma-94	228	6	(	(	PUNCT
ma-94	228	7	1994	1994	NUM
ma-94	228	8	)	)	PUNCT
ma-94	228	9	20	20	NUM
ma-94	228	10	-	-	SYM
ma-94	228	11	24	24	NUM
ma-94	228	12	.	.	PUNCT
ma-94	229	1	(	(	PUNCT
ma-94	229	2	in	in	ADP
ma-94	229	3	russian).[13	russian).[13	PROPN
ma-94	229	4	]	]	PUNCT
ma-94	229	5	j.	j.	PROPN
ma-94	229	6	rokne	rokne	PROPN
ma-94	229	7	,	,	PUNCT
ma-94	229	8	newton	newton	PROPN
ma-94	229	9	’s	’s	PART
ma-94	229	10	method	method	NOUN
ma-94	229	11	under	under	ADP
ma-94	229	12	mild	mild	ADJ
ma-94	229	13	differentiability	differentiability	NOUN
ma-94	229	14	conditions	condition	NOUN
ma-94	229	15	with	with	ADP
ma-94	229	16	error	error	NOUN
ma-94	229	17	analysis	analysis	NOUN
ma-94	229	18	,	,	PUNCT
ma-94	229	19	numer	numer	NOUN
ma-94	229	20	.	.	PROPN
ma-94	229	21	math	math	NOUN
ma-94	229	22	.	.	PUNCT
ma-94	230	1	18	18	NUM
ma-94	230	2	(	(	PUNCT
ma-94	230	3	1971)401–412	1971)401–412	NUM
ma-94	230	4	.	.	PUNCT
ma-94	230	5	https://doi.org/10.1007/bf01406677.[14	https://doi.org/10.1007/bf01406677.[14	PROPN
ma-94	230	6	]	]	PUNCT
ma-94	230	7	b.a	b.a	PROPN
ma-94	230	8	.	.	PROPN
ma-94	230	9	vertgeim	vertgeim	PROPN
ma-94	230	10	,	,	PUNCT
ma-94	230	11	on	on	ADP
ma-94	230	12	some	some	DET
ma-94	230	13	methods	method	NOUN
ma-94	230	14	of	of	ADP
ma-94	230	15	the	the	DET
ma-94	230	16	approximate	approximate	ADJ
ma-94	230	17	solution	solution	NOUN
ma-94	230	18	of	of	ADP
ma-94	230	19	nonlinear	nonlinear	ADJ
ma-94	230	20	functional	functional	ADJ
ma-94	230	21	equations	equation	NOUN
ma-94	230	22	in	in	ADP
ma-94	230	23	banach	banach	NOUN
ma-94	230	24	spaces	space	NOUN
ma-94	231	1	,	,	PUNCT
ma-94	231	2	uspekhi	uspekhi	PROPN
ma-94	231	3	mat	mat	PROPN
ma-94	231	4	.	.	PUNCT
ma-94	231	5	nauk	nauk	PROPN
ma-94	231	6	.	.	PROPN
ma-94	232	1	12	12	NUM
ma-94	232	2	(	(	PUNCT
ma-94	232	3	1957	1957	NUM
ma-94	232	4	)	)	PUNCT
ma-94	232	5	166	166	NUM
ma-94	232	6	-	-	SYM
ma-94	232	7	169	169	NUM
ma-94	232	8	(	(	PUNCT
ma-94	232	9	in	in	ADP
ma-94	232	10	russian	russian	NOUN
ma-94	232	11	)	)	PUNCT
ma-94	232	12	.	.	PUNCT
ma-94	233	1	engl	engl	PROPN
ma-94	233	2	.	.	PUNCT
ma-94	234	1	transl	transl	PROPN
ma-94	234	2	:	:	PUNCT
ma-94	234	3	amer	amer	PROPN
ma-94	234	4	.	.	PROPN
ma-94	234	5	math	math	PROPN
ma-94	234	6	.	.	PUNCT
ma-94	235	1	soc	soc	PROPN
ma-94	235	2	.	.	PUNCT
ma-94	236	1	transl	transl	PROPN
ma-94	236	2	.	.	PUNCT
ma-94	237	1	16	16	NUM
ma-94	237	2	(	(	PUNCT
ma-94	237	3	1960	1960	NUM
ma-94	237	4	)	)	PUNCT
ma-94	237	5	378	378	NUM
ma-94	237	6	-	-	SYM
ma-94	237	7	382	382	NUM
ma-94	237	8	.	.	PUNCT
ma-94	238	1	https://doi.org/10.28924/ada/ma.2.18	https://doi.org/10.28924/ada/ma.2.18	PROPN
ma-94	238	2	https://doi.org/10.1016/j.jco.2010.08.006	https://doi.org/10.1016/j.jco.2010.08.006	PROPN
ma-94	238	3	https://doi.org/10.1016/j.jco.2010.08.006	https://doi.org/10.1016/j.jco.2010.08.006	NOUN
ma-94	238	4	https://doi.org/10.1007/978-0-387-72743-1	https://doi.org/10.1007/978-0-387-72743-1	PROPN
ma-94	238	5	https://doi.org/10.1007/978-0-387-72743-1	https://doi.org/10.1007/978-0-387-72743-1	PROPN
ma-94	238	6	https://doi.org/10.1081/nfa-120026367	https://doi.org/10.1081/nfa-120026367	X
ma-94	238	7	https://doi.org/10.1016/j.jmaa.2005.09.008	https://doi.org/10.1016/j.jmaa.2005.09.008	NOUN
ma-94	238	8	https://doi.org/10.4171/zaa/821	https://doi.org/10.4171/zaa/821	NOUN
ma-94	238	9	https://doi.org/10.1007/978-3-030-48702-7	https://doi.org/10.1007/978-3-030-48702-7	PROPN
ma-94	238	10	https://doi.org/10.1016/s0022-0000(70)80009-5	https://doi.org/10.1016/s0022-0000(70)80009-5	PROPN
ma-94	238	11	https://doi.org/10.1016/s0022-0000(70)80009-5	https://doi.org/10.1016/s0022-0000(70)80009-5	PROPN
ma-94	238	12	https://doi.org/10.1007/bf01406677	https://doi.org/10.1007/bf01406677	PRON
ma-94	239	1	1	1	NUM
ma-94	239	2	.	.	PUNCT
ma-94	239	3	introduction	introduction	NOUN
ma-94	239	4	2	2	NUM
ma-94	239	5	.	.	PUNCT
ma-94	239	6	convergence	convergence	NOUN
ma-94	239	7	references	reference	NOUN