id	sid	tid	token	lemma	pos
ma-104	1	1	2023	2023	NUM
ma-104	1	2	ada	ada	PROPN
ma-104	1	3	academica	academica	PROPN
ma-104	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-104	1	5	.	.	PUNCT
ma-104	2	1	j.	j.	PROPN
ma-104	2	2	math	math	PROPN
ma-104	2	3	.	.	PUNCT
ma-104	3	1	anal	anal	ADJ
ma-104	3	2	.	.	PUNCT
ma-104	4	1	3	3	NUM
ma-104	4	2	(	(	PUNCT
ma-104	4	3	2023	2023	NUM
ma-104	4	4	)	)	PUNCT
ma-104	5	1	5doi	5doi	NOUN
ma-104	5	2	:	:	PUNCT
ma-104	5	3	10.28924	10.28924	NUM
ma-104	5	4	/	/	SYM
ma-104	5	5	ada	ada	PROPN
ma-104	5	6	/	/	SYM
ma-104	5	7	ma.3.5	ma.3.5	PROPN
ma-104	5	8	updated	update	VERB
ma-104	5	9	and	and	CCONJ
ma-104	5	10	weaker	weak	ADJ
ma-104	5	11	convergence	convergence	NOUN
ma-104	5	12	criteria	criterion	NOUN
ma-104	5	13	of	of	ADP
ma-104	5	14	newton	newton	PROPN
ma-104	5	15	iterates	iterate	VERB
ma-104	5	16	for	for	ADP
ma-104	5	17	equations	equation	NOUN
ma-104	5	18	samundra	samundra	VERB
ma-104	5	19	regmi1	regmi1	PROPN
ma-104	5	20	,	,	PUNCT
ma-104	5	21	ioannis	ioannis	PROPN
ma-104	5	22	k.	k.	PROPN
ma-104	5	23	argyros2,∗	argyros2,∗	PROPN
ma-104	5	24	,	,	PUNCT
ma-104	5	25	santhosh	santhosh	PROPN
ma-104	5	26	george3	george3	PROPN
ma-104	5	27	,	,	PUNCT
ma-104	5	28	michael	michael	PROPN
ma-104	5	29	i.	i.	PROPN
ma-104	5	30	argyros4	argyros4	PROPN
ma-104	6	1	1department	1department	NUM
ma-104	6	2	of	of	ADP
ma-104	6	3	mathematics	mathematic	NOUN
ma-104	6	4	,	,	PUNCT
ma-104	6	5	university	university	PROPN
ma-104	6	6	of	of	ADP
ma-104	6	7	houston	houston	PROPN
ma-104	6	8	,	,	PUNCT
ma-104	6	9	houston	houston	PROPN
ma-104	6	10	,	,	PUNCT
ma-104	6	11	tx	tx	PROPN
ma-104	6	12	77204	77204	NUM
ma-104	6	13	,	,	PUNCT
ma-104	6	14	usa	usa	PROPN
ma-104	6	15	sregmi5@uh.edu	sregmi5@uh.edu	PROPN
ma-104	7	1	2department	2department	NUM
ma-104	7	2	of	of	ADP
ma-104	7	3	mathematical	mathematical	ADJ
ma-104	7	4	sciences	sciences	PROPN
ma-104	7	5	,	,	PUNCT
ma-104	7	6	cameron	cameron	PROPN
ma-104	7	7	university	university	PROPN
ma-104	7	8	,	,	PUNCT
ma-104	7	9	lawton	lawton	PROPN
ma-104	7	10	,	,	PUNCT
ma-104	7	11	ok	ok	PROPN
ma-104	7	12	73505	73505	NUM
ma-104	7	13	,	,	PUNCT
ma-104	7	14	usa	usa	PROPN
ma-104	7	15	iargyros@cameron.edu	iargyros@cameron.edu	PROPN
ma-104	8	1	3department	3department	NUM
ma-104	8	2	of	of	ADP
ma-104	8	3	mathematical	mathematical	ADJ
ma-104	8	4	and	and	CCONJ
ma-104	8	5	computational	computational	ADJ
ma-104	8	6	sciences	science	NOUN
ma-104	8	7	,	,	PUNCT
ma-104	8	8	national	national	PROPN
ma-104	8	9	institute	institute	PROPN
ma-104	8	10	of	of	ADP
ma-104	8	11	technology	technology	PROPN
ma-104	8	12	karnataka	karnataka	PROPN
ma-104	8	13	,	,	PUNCT
ma-104	8	14	india-575	india-575	ADJ
ma-104	8	15	025	025	NUM
ma-104	8	16	sgeorge@nitk.edu.in	sgeorge@nitk.edu.in	NOUN
ma-104	8	17	4university	4university	PROPN
ma-104	8	18	of	of	ADP
ma-104	8	19	oklahoma	oklahoma	PROPN
ma-104	8	20	,	,	PUNCT
ma-104	8	21	department	department	NOUN
ma-104	8	22	of	of	ADP
ma-104	8	23	computer	computer	NOUN
ma-104	8	24	science	science	PROPN
ma-104	8	25	,	,	PUNCT
ma-104	8	26	norman	norman	PROPN
ma-104	8	27	,	,	PUNCT
ma-104	8	28	ok	ok	ADJ
ma-104	8	29	73019	73019	NUM
ma-104	8	30	,	,	PUNCT
ma-104	8	31	usa	usa	PROPN
ma-104	8	32	michael.i.argyros-1@ou.edu	michael.i.argyros-1@ou.edu	PROPN
ma-104	8	33	∗correspondence	∗correspondence	NOUN
ma-104	8	34	:	:	PUNCT
ma-104	8	35	iargyros@cameron.edu	iargyros@cameron.edu	X
ma-104	9	1	abstract	abstract	ADJ
ma-104	9	2	.	.	PUNCT
ma-104	10	1	newton	newton	PROPN
ma-104	10	2	iteration	iteration	PROPN
ma-104	10	3	is	be	AUX
ma-104	10	4	often	often	ADV
ma-104	10	5	used	use	VERB
ma-104	10	6	as	as	ADP
ma-104	10	7	a	a	DET
ma-104	10	8	solver	solver	NOUN
ma-104	10	9	for	for	ADP
ma-104	10	10	nonlinear	nonlinear	ADJ
ma-104	10	11	equations	equation	NOUN
ma-104	10	12	in	in	ADP
ma-104	10	13	abstract	abstract	ADJ
ma-104	10	14	spaces.some	spaces.some	NUM
ma-104	10	15	of	of	ADP
ma-104	10	16	the	the	DET
ma-104	10	17	main	main	ADJ
ma-104	10	18	concerns	concern	NOUN
ma-104	10	19	are	be	AUX
ma-104	10	20	general	general	ADJ
ma-104	10	21	:	:	PUNCT
ma-104	10	22	criteria	criterion	NOUN
ma-104	10	23	for	for	ADP
ma-104	10	24	convergence	convergence	NOUN
ma-104	10	25	,	,	PUNCT
ma-104	10	26	error	error	NOUN
ma-104	10	27	estimations	estimation	NOUN
ma-104	10	28	on	on	ADP
ma-104	10	29	consecutiveiterates	consecutiveiterate	NOUN
ma-104	10	30	,	,	PUNCT
ma-104	10	31	and	and	CCONJ
ma-104	10	32	the	the	DET
ma-104	10	33	location	location	NOUN
ma-104	10	34	of	of	ADP
ma-104	10	35	a	a	DET
ma-104	10	36	solution	solution	NOUN
ma-104	10	37	.	.	PUNCT
ma-104	11	1	a	a	DET
ma-104	11	2	plethora	plethora	NOUN
ma-104	11	3	of	of	ADP
ma-104	11	4	authors	author	NOUN
ma-104	11	5	has	have	AUX
ma-104	11	6	addressed	address	VERB
ma-104	11	7	these	these	DET
ma-104	11	8	concerns	concern	NOUN
ma-104	11	9	by	by	ADP
ma-104	11	10	pre	pre	ADJ
ma-104	11	11	-	-	ADJ
ma-104	11	12	senting	senting	ADJ
ma-104	11	13	results	result	NOUN
ma-104	11	14	based	base	VERB
ma-104	11	15	on	on	ADP
ma-104	11	16	the	the	DET
ma-104	11	17	celebrated	celebrated	ADJ
ma-104	11	18	kantorovich	kantorovich	PROPN
ma-104	11	19	theory	theory	NOUN
ma-104	11	20	.	.	PUNCT
ma-104	12	1	this	this	DET
ma-104	12	2	article	article	NOUN
ma-104	12	3	contributes	contribute	VERB
ma-104	12	4	in	in	ADP
ma-104	12	5	this	this	DET
ma-104	12	6	directionby	directionby	NOUN
ma-104	12	7	extending	extend	VERB
ma-104	12	8	earlier	early	ADJ
ma-104	12	9	results	result	NOUN
ma-104	12	10	but	but	CCONJ
ma-104	12	11	without	without	ADP
ma-104	12	12	additional	additional	ADJ
ma-104	12	13	conditions	condition	NOUN
ma-104	12	14	.	.	PUNCT
ma-104	13	1	these	these	DET
ma-104	13	2	extensions	extension	NOUN
ma-104	13	3	become	become	AUX
ma-104	13	4	possibleusing	possibleuse	VERB
ma-104	13	5	a	a	DET
ma-104	13	6	more	more	ADV
ma-104	13	7	precise	precise	ADJ
ma-104	13	8	majorization	majorization	NOUN
ma-104	13	9	than	than	ADP
ma-104	13	10	the	the	DET
ma-104	13	11	one	one	NOUN
ma-104	13	12	given	give	VERB
ma-104	13	13	in	in	ADP
ma-104	13	14	earlier	early	ADJ
ma-104	13	15	articles	article	NOUN
ma-104	13	16	.	.	PUNCT
ma-104	14	1	numerical	numerical	PROPN
ma-104	14	2	experimentationcomplements	experimentationcomplements	PROPN
ma-104	14	3	the	the	DET
ma-104	14	4	theoretical	theoretical	ADJ
ma-104	14	5	results	result	NOUN
ma-104	14	6	involving	involve	VERB
ma-104	14	7	a	a	DET
ma-104	14	8	partial	partial	ADJ
ma-104	14	9	differential	differential	NOUN
ma-104	14	10	and	and	CCONJ
ma-104	14	11	an	an	DET
ma-104	14	12	integral	integral	ADJ
ma-104	14	13	equation	equation	NOUN
ma-104	14	14	.	.	PUNCT
ma-104	15	1	1	1	X
ma-104	15	2	.	.	X
ma-104	15	3	introduction	introduction	NOUN
ma-104	15	4	nonlinear	nonlinear	ADJ
ma-104	15	5	equation	equation	NOUN
ma-104	15	6	f	f	X
ma-104	15	7	(	(	PUNCT
ma-104	15	8	x	x	X
ma-104	15	9	)	)	PUNCT
ma-104	15	10	=	=	SYM
ma-104	15	11	0	0	NUM
ma-104	15	12	,	,	PUNCT
ma-104	15	13	(	(	PUNCT
ma-104	15	14	1.1)plays	1.1)plays	NUM
ma-104	15	15	a	a	DET
ma-104	15	16	important	important	ADJ
ma-104	15	17	role	role	NOUN
ma-104	15	18	due	due	ADP
ma-104	15	19	to	to	ADP
ma-104	15	20	the	the	DET
ma-104	15	21	fact	fact	NOUN
ma-104	15	22	that	that	SCONJ
ma-104	15	23	many	many	ADJ
ma-104	15	24	applications	application	NOUN
ma-104	15	25	can	can	AUX
ma-104	15	26	be	be	AUX
ma-104	15	27	brought	bring	VERB
ma-104	15	28	to	to	PART
ma-104	15	29	look	look	VERB
ma-104	15	30	like	like	ADP
ma-104	15	31	it	it	PRON
ma-104	15	32	.	.	PUNCT
ma-104	16	1	thecelebrated	thecelebrate	VERB
ma-104	16	2	newton	newton	PROPN
ma-104	16	3	iteration	iteration	PROPN
ma-104	16	4	(	(	PUNCT
ma-104	16	5	ni	ni	PROPN
ma-104	16	6	)	)	PUNCT
ma-104	16	7	in	in	ADP
ma-104	16	8	the	the	DET
ma-104	16	9	following	follow	VERB
ma-104	16	10	form	form	NOUN
ma-104	16	11	xn+1	xn+1	PROPN
ma-104	17	1	=	=	SYM
ma-104	17	2	xn	xn	PROPN
ma-104	18	1	−	−	PROPN
ma-104	18	2	f	f	PROPN
ma-104	18	3	′(xn)−1f	′(xn)−1f	PROPN
ma-104	18	4	(	(	PUNCT
ma-104	18	5	xn	xn	PROPN
ma-104	18	6	)	)	PUNCT
ma-104	18	7	,	,	PUNCT
ma-104	18	8	∀	∀	X
ma-104	18	9	n	n	NOUN
ma-104	18	10	=	=	SYM
ma-104	18	11	0	0	NUM
ma-104	18	12	,	,	PUNCT
ma-104	18	13	1	1	NUM
ma-104	18	14	,	,	PUNCT
ma-104	18	15	2	2	NUM
ma-104	18	16	,	,	PUNCT
ma-104	18	17	.	.	PUNCT
ma-104	18	18	.	.	PUNCT
ma-104	18	19	.	.	PUNCT
ma-104	19	1	(	(	PUNCT
ma-104	19	2	1.2	1.2	NUM
ma-104	19	3	)	)	PUNCT
ma-104	19	4	is	be	AUX
ma-104	19	5	often	often	ADV
ma-104	19	6	applied	apply	VERB
ma-104	19	7	to	to	PART
ma-104	19	8	solve	solve	VERB
ma-104	19	9	equation	equation	NOUN
ma-104	19	10	(	(	PUNCT
ma-104	19	11	1.1	1.1	NUM
ma-104	19	12	)	)	PUNCT
ma-104	19	13	iteratively	iteratively	ADV
ma-104	19	14	.	.	PUNCT
ma-104	20	1	here	here	ADV
ma-104	20	2	,	,	PUNCT
ma-104	20	3	f	f	PROPN
ma-104	20	4	:	:	PUNCT
ma-104	20	5	ω	ω	NUM
ma-104	20	6	⊂	⊂	PROPN
ma-104	20	7	m1	m1	PROPN
ma-104	20	8	−→	−→	NOUN
ma-104	20	9	m2	m2	PROPN
ma-104	20	10	is	be	AUX
ma-104	20	11	differentiable	differentiable	ADJ
ma-104	20	12	perfréchet	perfréchet	NOUN
ma-104	20	13	and	and	CCONJ
ma-104	20	14	operates	operate	VERB
ma-104	20	15	between	between	ADP
ma-104	20	16	banach	banach	NOUN
ma-104	20	17	spaces	space	NOUN
ma-104	20	18	m1	m1	PROPN
ma-104	20	19	and	and	CCONJ
ma-104	20	20	m2	m2	PROPN
ma-104	20	21	,	,	PUNCT
ma-104	20	22	whereas	whereas	SCONJ
ma-104	20	23	set	set	VERB
ma-104	20	24	ω	ω	PROPN
ma-104	20	25	6=	6=	PROPN
ma-104	20	26	∅.kantorovich	∅.kantorovich	PROPN
ma-104	20	27	inaugurated	inaugurate	VERB
ma-104	20	28	the	the	DET
ma-104	20	29	semi	semi	ADJ
ma-104	20	30	-	-	ADJ
ma-104	20	31	local	local	ADJ
ma-104	20	32	convergence	convergence	NOUN
ma-104	20	33	of	of	ADP
ma-104	20	34	ni	ni	PROPN
ma-104	20	35	(	(	PUNCT
ma-104	20	36	slcni	slcni	ADJ
ma-104	20	37	)	)	PUNCT
ma-104	20	38	analysis	analysis	NOUN
ma-104	20	39	of	of	ADP
ma-104	20	40	ni	ni	PROPN
ma-104	20	41	in	in	ADP
ma-104	20	42	abstractspaces	abstractspace	NOUN
ma-104	20	43	by	by	ADP
ma-104	20	44	applying	apply	VERB
ma-104	20	45	the	the	DET
ma-104	20	46	contraction	contraction	NOUN
ma-104	20	47	mapping	mapping	NOUN
ma-104	20	48	principle	principle	NOUN
ma-104	20	49	due	due	ADP
ma-104	20	50	to	to	ADP
ma-104	20	51	banach	banach	ADV
ma-104	20	52	.	.	PUNCT
ma-104	21	1	he	he	PRON
ma-104	21	2	presented	present	VERB
ma-104	21	3	two	two	NUM
ma-104	21	4	different	different	ADJ
ma-104	21	5	received	receive	VERB
ma-104	21	6	:	:	PUNCT
ma-104	21	7	29	29	NUM
ma-104	21	8	apr	apr	NOUN
ma-104	21	9	2022	2022	NUM
ma-104	21	10	.	.	PUNCT
ma-104	22	1	key	key	ADJ
ma-104	22	2	words	word	NOUN
ma-104	22	3	and	and	CCONJ
ma-104	22	4	phrases	phrase	NOUN
ma-104	22	5	.	.	PUNCT
ma-104	23	1	iterative	iterative	NOUN
ma-104	23	2	processes	process	NOUN
ma-104	23	3	;	;	PUNCT
ma-104	23	4	newton	newton	PROPN
ma-104	23	5	iteration	iteration	NOUN
ma-104	23	6	;	;	PUNCT
ma-104	23	7	banach	banach	NOUN
ma-104	23	8	space	space	NOUN
ma-104	23	9	;	;	PUNCT
ma-104	23	10	semi	semi	ADJ
ma-104	23	11	-	-	ADJ
ma-104	23	12	local	local	ADJ
ma-104	23	13	convergence.1	convergence.1	PROPN
ma-104	23	14	https://adac.ee	https://adac.ee	PROPN
ma-104	23	15	https://doi.org/10.28924/ada/ma.3.5	https://doi.org/10.28924/ada/ma.3.5	PROPN
ma-104	23	16	eur	eur	PROPN
ma-104	23	17	.	.	PUNCT
ma-104	24	1	j.	j.	PROPN
ma-104	24	2	math	math	PROPN
ma-104	24	3	.	.	PUNCT
ma-104	25	1	anal	anal	PROPN
ma-104	25	2	.	.	PUNCT
ma-104	26	1	10.28924	10.28924	NUM
ma-104	26	2	/	/	SYM
ma-104	26	3	ada	ada	PROPN
ma-104	26	4	/	/	SYM
ma-104	26	5	ma.3.5	ma.3.5	PROPN
ma-104	26	6	2proofs	2proofs	NUM
ma-104	26	7	based	base	VERB
ma-104	26	8	on	on	ADP
ma-104	26	9	majorization	majorization	NOUN
ma-104	26	10	and	and	CCONJ
ma-104	26	11	recurrent	recurrent	ADJ
ma-104	26	12	relations	relation	NOUN
ma-104	27	1	[	[	X
ma-104	27	2	12	12	NUM
ma-104	27	3	]	]	PUNCT
ma-104	27	4	.	.	PUNCT
ma-104	28	1	the	the	PRON
ma-104	28	2	newton	newton	PROPN
ma-104	28	3	-	-	PUNCT
ma-104	28	4	kantorovich	kantorovich	PROPN
ma-104	28	5	theorem	theorem	PROPN
ma-104	28	6	givesthe	givesthe	PROPN
ma-104	28	7	slcni	slcni	PROPN
ma-104	28	8	.	.	PUNCT
ma-104	29	1	numerous	numerous	ADJ
ma-104	29	2	authors	author	NOUN
ma-104	29	3	applied	apply	VERB
ma-104	29	4	this	this	DET
ma-104	29	5	result	result	NOUN
ma-104	29	6	,	,	PUNCT
ma-104	29	7	in	in	ADP
ma-104	29	8	applications	application	NOUN
ma-104	29	9	and	and	CCONJ
ma-104	29	10	also	also	ADV
ma-104	29	11	as	as	ADP
ma-104	29	12	a	a	DET
ma-104	29	13	theoretical	theoretical	ADJ
ma-104	29	14	tool.even	tool.even	NUM
ma-104	29	15	a	a	DET
ma-104	29	16	simple	simple	ADJ
ma-104	29	17	equation	equation	NOUN
ma-104	29	18	given	give	VERB
ma-104	29	19	in	in	ADP
ma-104	29	20	[	[	X
ma-104	29	21	1–4	1–4	PROPN
ma-104	29	22	,	,	PUNCT
ma-104	29	23	7	7	NUM
ma-104	29	24	,	,	PUNCT
ma-104	29	25	10	10	NUM
ma-104	29	26	,	,	PUNCT
ma-104	29	27	11	11	NUM
ma-104	29	28	]	]	PUNCT
ma-104	29	29	shows	show	VERB
ma-104	29	30	that	that	SCONJ
ma-104	29	31	convergence	convergence	NOUN
ma-104	29	32	criteria	criterion	NOUN
ma-104	29	33	may	may	AUX
ma-104	29	34	not	not	PART
ma-104	29	35	besatisfied	besatisfie	VERB
ma-104	29	36	.	.	PUNCT
ma-104	30	1	however	however	ADV
ma-104	30	2	,	,	PUNCT
ma-104	30	3	ni	ni	PROPN
ma-104	30	4	may	may	AUX
ma-104	30	5	be	be	AUX
ma-104	30	6	convergent	convergent	ADJ
ma-104	30	7	(	(	PUNCT
ma-104	30	8	see	see	VERB
ma-104	30	9	the	the	DET
ma-104	30	10	numerical	numerical	ADJ
ma-104	30	11	section	section	NOUN
ma-104	30	12	,	,	PUNCT
ma-104	30	13	example	example	NOUN
ma-104	30	14	4.1	4.1	NUM
ma-104	30	15	)	)	PUNCT
ma-104	30	16	.	.	PUNCT
ma-104	31	1	that	that	PRON
ma-104	31	2	iswhy	iswhy	ADP
ma-104	31	3	these	these	DET
ma-104	31	4	criteria	criterion	NOUN
ma-104	31	5	are	be	AUX
ma-104	31	6	weakened	weaken	VERB
ma-104	31	7	in	in	ADP
ma-104	31	8	[	[	X
ma-104	31	9	2–4	2–4	NUM
ma-104	31	10	]	]	X
ma-104	31	11	.	.	PUNCT
ma-104	32	1	but	but	CCONJ
ma-104	32	2	no	no	DET
ma-104	32	3	new	new	ADJ
ma-104	32	4	conditions	condition	NOUN
ma-104	32	5	are	be	AUX
ma-104	32	6	added	add	VERB
ma-104	32	7	.	.	PUNCT
ma-104	33	1	in	in	ADP
ma-104	33	2	this	this	DET
ma-104	33	3	study	study	NOUN
ma-104	33	4	twoadditional	twoadditional	ADJ
ma-104	33	5	features	feature	NOUN
ma-104	33	6	are	be	AUX
ma-104	33	7	presented	present	VERB
ma-104	33	8	.	.	PUNCT
ma-104	34	1	one	one	NUM
ma-104	34	2	involves	involve	VERB
ma-104	34	3	an	an	DET
ma-104	34	4	explicit	explicit	ADJ
ma-104	34	5	upper	upper	ADJ
ma-104	34	6	bound	bind	VERB
ma-104	34	7	on	on	ADP
ma-104	34	8	the	the	DET
ma-104	34	9	smallness	smallness	NOUN
ma-104	34	10	of	of	ADP
ma-104	34	11	initialapproximation	initialapproximation	NOUN
ma-104	34	12	.	.	PUNCT
ma-104	35	1	moreover	moreover	ADV
ma-104	35	2	by	by	ADP
ma-104	35	3	choosing	choose	VERB
ma-104	35	4	a	a	DET
ma-104	35	5	bit	bit	NOUN
ma-104	35	6	larger	large	ADJ
ma-104	35	7	bound	bind	VERB
ma-104	35	8	the	the	DET
ma-104	35	9	convergence	convergence	NOUN
ma-104	35	10	order	order	NOUN
ma-104	35	11	of	of	ADP
ma-104	35	12	ni	ni	PROPN
ma-104	35	13	is	be	AUX
ma-104	35	14	recovered.consequently	recovered.consequently	ADV
ma-104	35	15	,	,	PUNCT
ma-104	35	16	new	new	ADJ
ma-104	35	17	results	result	NOUN
ma-104	35	18	can	can	AUX
ma-104	35	19	always	always	ADV
ma-104	35	20	replace	replace	VERB
ma-104	35	21	corresponding	corresponding	ADJ
ma-104	35	22	ones	one	NOUN
ma-104	35	23	by	by	ADP
ma-104	35	24	kantorovich	kantorovich	PROPN
ma-104	36	1	[	[	X
ma-104	36	2	7	7	NUM
ma-104	36	3	]	]	PUNCT
ma-104	36	4	and	and	CCONJ
ma-104	36	5	others[5,8–11	others[5,8–11	PROPN
ma-104	36	6	]	]	PUNCT
ma-104	36	7	,	,	PUNCT
ma-104	36	8	since	since	SCONJ
ma-104	36	9	preceding	precede	VERB
ma-104	36	10	results	result	NOUN
ma-104	36	11	imply	imply	VERB
ma-104	36	12	the	the	DET
ma-104	36	13	one	one	NOUN
ma-104	36	14	in	in	ADP
ma-104	36	15	this	this	DET
ma-104	36	16	study	study	NOUN
ma-104	36	17	but	but	CCONJ
ma-104	36	18	not	not	PART
ma-104	36	19	necessarily	necessarily	ADV
ma-104	36	20	vice	vice	ADV
ma-104	36	21	versa	versa	ADV
ma-104	36	22	.	.	PUNCT
ma-104	37	1	methodin	methodin	VERB
ma-104	37	2	this	this	DET
ma-104	37	3	study	study	NOUN
ma-104	37	4	uses	use	VERB
ma-104	37	5	smaller	small	ADJ
ma-104	37	6	lipschitz	lipschitz	NOUN
ma-104	37	7	or	or	CCONJ
ma-104	37	8	hölder	hölder	VERB
ma-104	37	9	parameters	parameter	NOUN
ma-104	37	10	to	to	PART
ma-104	37	11	achieve	achieve	VERB
ma-104	37	12	these	these	DET
ma-104	37	13	extensions	extension	NOUN
ma-104	37	14	which	which	PRON
ma-104	37	15	arespecializations	arespecialization	NOUN
ma-104	37	16	of	of	ADP
ma-104	37	17	earlier	early	ADJ
ma-104	37	18	ones	one	NOUN
ma-104	37	19	.	.	PUNCT
ma-104	38	1	that	that	PRON
ma-104	38	2	is	be	AUX
ma-104	38	3	no	no	DET
ma-104	38	4	additional	additional	ADJ
ma-104	38	5	effort	effort	NOUN
ma-104	38	6	is	be	AUX
ma-104	38	7	needed	need	VERB
ma-104	38	8	.	.	PUNCT
ma-104	39	1	the	the	DET
ma-104	39	2	generality	generality	NOUN
ma-104	39	3	of	of	ADP
ma-104	39	4	this	this	PRON
ma-104	39	5	ideaallows	ideaallow	VERB
ma-104	39	6	its	its	PRON
ma-104	39	7	application	application	NOUN
ma-104	39	8	on	on	ADP
ma-104	39	9	other	other	ADJ
ma-104	39	10	processes	process	NOUN
ma-104	39	11	[	[	X
ma-104	39	12	3	3	NUM
ma-104	39	13	,	,	PUNCT
ma-104	39	14	4	4	NUM
ma-104	39	15	,	,	PUNCT
ma-104	39	16	11].contributions	11].contribution	NOUN
ma-104	39	17	by	by	ADP
ma-104	39	18	others	other	NOUN
ma-104	39	19	can	can	AUX
ma-104	39	20	be	be	AUX
ma-104	39	21	found	find	VERB
ma-104	39	22	in	in	ADP
ma-104	39	23	section	section	NOUN
ma-104	39	24	4	4	NUM
ma-104	39	25	,	,	PUNCT
ma-104	39	26	where	where	SCONJ
ma-104	39	27	comparisons	comparison	NOUN
ma-104	39	28	take	take	VERB
ma-104	39	29	place	place	NOUN
ma-104	39	30	.	.	PUNCT
ma-104	40	1	the	the	DET
ma-104	40	2	majoriza	majoriza	NOUN
ma-104	40	3	-	-	PUNCT
ma-104	40	4	tion	tion	NOUN
ma-104	40	5	of	of	ADP
ma-104	40	6	ni	ni	PROPN
ma-104	40	7	is	be	AUX
ma-104	40	8	discussed	discuss	VERB
ma-104	40	9	in	in	ADP
ma-104	40	10	section	section	NOUN
ma-104	40	11	2	2	NUM
ma-104	40	12	.	.	PUNCT
ma-104	41	1	slcni	slcni	PROPN
ma-104	41	2	appears	appear	VERB
ma-104	41	3	in	in	ADP
ma-104	41	4	section	section	NOUN
ma-104	41	5	3	3	NUM
ma-104	41	6	.	.	PUNCT
ma-104	42	1	the	the	DET
ma-104	42	2	numerical	numerical	ADJ
ma-104	42	3	experimentationis	experimentationis	NOUN
ma-104	42	4	given	give	VERB
ma-104	42	5	in	in	ADP
ma-104	42	6	section4	section4	PROPN
ma-104	42	7	.	.	PUNCT
ma-104	43	1	conclusions	conclusion	NOUN
ma-104	43	2	complete	complete	VERB
ma-104	43	3	this	this	DET
ma-104	43	4	study	study	NOUN
ma-104	43	5	in	in	ADP
ma-104	43	6	section	section	NOUN
ma-104	43	7	5	5	NUM
ma-104	43	8	.	.	NOUN
ma-104	43	9	2	2	NUM
ma-104	43	10	.	.	X
ma-104	43	11	majorization	majorization	NOUN
ma-104	43	12	of	of	ADP
ma-104	43	13	ni	ni	PROPN
ma-104	43	14	let	let	VERB
ma-104	43	15	k0	k0	PROPN
ma-104	43	16	,	,	PUNCT
ma-104	43	17	k	k	PROPN
ma-104	43	18	,	,	PUNCT
ma-104	43	19	l0	l0	PROPN
ma-104	43	20	,	,	PUNCT
ma-104	43	21	l	l	NOUN
ma-104	43	22	denote	denote	VERB
ma-104	43	23	positive	positive	ADJ
ma-104	43	24	numbers	number	NOUN
ma-104	43	25	,	,	PUNCT
ma-104	43	26	q	q	NOUN
ma-104	43	27	∈	∈	PROPN
ma-104	43	28	(	(	PUNCT
ma-104	43	29	0	0	NUM
ma-104	43	30	,	,	PUNCT
ma-104	43	31	1	1	NUM
ma-104	43	32	]	]	PUNCT
ma-104	43	33	and	and	CCONJ
ma-104	43	34	t	t	PROPN
ma-104	43	35	stand	stand	VERB
ma-104	43	36	for	for	ADP
ma-104	43	37	a	a	DET
ma-104	43	38	positive	positive	ADJ
ma-104	43	39	variable	variable	NOUN
ma-104	43	40	.	.	PUNCT
ma-104	44	1	theseparametrs	theseparametrs	PROPN
ma-104	44	2	are	be	AUX
ma-104	44	3	connected	connect	VERB
ma-104	44	4	in	in	ADP
ma-104	44	5	section	section	NOUN
ma-104	44	6	3	3	NUM
ma-104	44	7	to	to	ADP
ma-104	44	8	initial	initial	ADJ
ma-104	44	9	data	datum	NOUN
ma-104	44	10	d	d	NOUN
ma-104	44	11	=	=	SYM
ma-104	44	12	(	(	PUNCT
ma-104	44	13	ω	ω	PROPN
ma-104	44	14	,	,	PUNCT
ma-104	44	15	y	y	PROPN
ma-104	44	16	,	,	PUNCT
ma-104	44	17	f	f	PROPN
ma-104	44	18	,	,	PUNCT
ma-104	44	19	f	f	PROPN
ma-104	44	20	′	′	NOUN
ma-104	44	21	,	,	PUNCT
ma-104	44	22	x0	x0	PROPN
ma-104	44	23	)	)	PUNCT
ma-104	44	24	.	.	PUNCT
ma-104	45	1	define	define	VERB
ma-104	45	2	sequence	sequence	NOUN
ma-104	45	3	{	{	PUNCT
ma-104	45	4	sn}by	sn}by	NOUN
ma-104	45	5	s0	s0	PROPN
ma-104	45	6	=	=	SYM
ma-104	45	7	0	0	NUM
ma-104	45	8	,	,	PUNCT
ma-104	45	9	s1(t	s1(t	X
ma-104	45	10	)	)	PUNCT
ma-104	45	11	=	=	SYM
ma-104	45	12	s1	s1	PROPN
ma-104	45	13	=	=	SYM
ma-104	45	14	t	t	PROPN
ma-104	45	15	s2(t	s2(t	PROPN
ma-104	45	16	)	)	PUNCT
ma-104	45	17	=	=	SYM
ma-104	45	18	s2	s2	NOUN
ma-104	45	19	=	=	SYM
ma-104	45	20	s1	s1	PROPN
ma-104	45	21	+	+	CCONJ
ma-104	45	22	k(s1	k(s1	NOUN
ma-104	45	23	−	−	PROPN
ma-104	45	24	s0)1+q	s0)1+q	PROPN
ma-104	45	25	(	(	PUNCT
ma-104	45	26	1	1	NUM
ma-104	45	27	+	+	NUM
ma-104	45	28	q)(1−k0sq1	q)(1−k0sq1	NUM
ma-104	45	29	)	)	PUNCT
ma-104	45	30	,	,	PUNCT
ma-104	45	31	sn+2(t	sn+2(t	NOUN
ma-104	45	32	)	)	PUNCT
ma-104	45	33	=	=	PUNCT
ma-104	45	34	sn+2	sn+2	PROPN
ma-104	45	35	=	=	SYM
ma-104	46	1	sn+1	sn+1	X
ma-104	46	2	+	+	CCONJ
ma-104	46	3	l(sn+1	l(sn+1	ADJ
ma-104	46	4	−	−	NOUN
ma-104	46	5	sn)1+q	sn)1+q	NOUN
ma-104	46	6	(	(	PUNCT
ma-104	46	7	1	1	NUM
ma-104	46	8	+	+	CCONJ
ma-104	46	9	q)(1−	q)(1−	PROPN
ma-104	46	10	l0sqn+1	l0sqn+1	NOUN
ma-104	46	11	)	)	PUNCT
ma-104	46	12	,	,	PUNCT
ma-104	46	13	∀n	∀n	NUM
ma-104	46	14	=	=	SYM
ma-104	46	15	1	1	NUM
ma-104	46	16	,	,	PUNCT
ma-104	46	17	2	2	NUM
ma-104	46	18	,	,	PUNCT
ma-104	46	19	.	.	PUNCT
ma-104	46	20	.	.	PUNCT
ma-104	46	21	.	.	PUNCT
ma-104	46	22	.	.	PUNCT
ma-104	47	1	(	(	PUNCT
ma-104	47	2	2.1	2.1	NUM
ma-104	47	3	)	)	PUNCT
ma-104	47	4	sequence	sequence	NOUN
ma-104	47	5	{	{	PUNCT
ma-104	47	6	xn	xn	PUNCT
ma-104	47	7	}	}	PUNCT
ma-104	47	8	is	be	AUX
ma-104	47	9	majorized	majorize	VERB
ma-104	47	10	by	by	ADP
ma-104	47	11	{	{	PUNCT
ma-104	47	12	sn	sn	NOUN
ma-104	47	13	}	}	PUNCT
ma-104	47	14	(	(	PUNCT
ma-104	47	15	see	see	VERB
ma-104	47	16	section	section	NOUN
ma-104	47	17	3	3	NUM
ma-104	47	18	)	)	PUNCT
ma-104	47	19	.	.	PUNCT
ma-104	48	1	that	that	PRON
ma-104	48	2	is	be	AUX
ma-104	48	3	why	why	SCONJ
ma-104	48	4	convergence	convergence	NOUN
ma-104	48	5	is	be	AUX
ma-104	48	6	studied	study	VERB
ma-104	48	7	first	first	ADJ
ma-104	48	8	forsequence	forsequence	NOUN
ma-104	48	9	{	{	PUNCT
ma-104	48	10	sn	sn	NOUN
ma-104	48	11	}	}	PUNCT
ma-104	48	12	.	.	PUNCT
ma-104	49	1	lemma	lemma	PROPN
ma-104	49	2	2.1	2.1	NUM
ma-104	49	3	.	.	PUNCT
ma-104	49	4	suppose	suppose	VERB
ma-104	49	5	k0	k0	PROPN
ma-104	49	6	t	t	PROPN
ma-104	49	7	q	q	X
ma-104	49	8	<	<	X
ma-104	49	9	1	1	NUM
ma-104	49	10	and	and	CCONJ
ma-104	49	11	l0s	l0s	PROPN
ma-104	49	12	q	q	X
ma-104	50	1	n+1	n+1	PROPN
ma-104	50	2	<	<	X
ma-104	50	3	1	1	NUM
ma-104	50	4	∀n	∀n	NUM
ma-104	50	5	=	=	SYM
ma-104	50	6	0	0	NUM
ma-104	50	7	,	,	PUNCT
ma-104	50	8	1	1	NUM
ma-104	50	9	,	,	PUNCT
ma-104	50	10	2	2	NUM
ma-104	50	11	,	,	PUNCT
ma-104	50	12	.	.	PUNCT
ma-104	50	13	.	.	PUNCT
ma-104	50	14	.	.	PUNCT
ma-104	50	15	.	.	PUNCT
ma-104	51	1	(	(	PUNCT
ma-104	51	2	2.2	2.2	NUM
ma-104	51	3	)	)	PUNCT
ma-104	51	4	then	then	ADV
ma-104	51	5	,	,	PUNCT
ma-104	51	6	sequence	sequence	NOUN
ma-104	51	7	{	{	PUNCT
ma-104	51	8	sn	sn	NOUN
ma-104	51	9	}	}	PUNCT
ma-104	51	10	is	be	AUX
ma-104	51	11	strictly	strictly	ADV
ma-104	51	12	increasing	increase	VERB
ma-104	51	13	and	and	CCONJ
ma-104	51	14	converges	converge	VERB
ma-104	51	15	to	to	ADP
ma-104	51	16	some	some	DET
ma-104	51	17	limit	limit	NOUN
ma-104	51	18	point	point	NOUN
ma-104	51	19	s∗	s∗	PROPN
ma-104	51	20	∈	∈	PROPN
ma-104	51	21	(	(	PUNCT
ma-104	51	22	0	0	NUM
ma-104	51	23	,	,	PUNCT
ma-104	51	24	(	(	PUNCT
ma-104	51	25	1l0	1l0	NUM
ma-104	51	26	)	)	PUNCT
ma-104	51	27	1	1	NUM
ma-104	51	28	q	q	NOUN
ma-104	51	29	]	]	X
ma-104	51	30	.	.	PUNCT
ma-104	52	1	the	the	DET
ma-104	52	2	point	point	NOUN
ma-104	52	3	s∗	s∗	PROPN
ma-104	52	4	is	be	AUX
ma-104	52	5	the	the	DET
ma-104	52	6	unique	unique	ADJ
ma-104	52	7	least	least	ADV
ma-104	52	8	upper	upper	ADJ
ma-104	52	9	bound	bind	VERB
ma-104	52	10	of	of	ADP
ma-104	52	11	sequence	sequence	NOUN
ma-104	52	12	{	{	PUNCT
ma-104	52	13	sn	sn	NOUN
ma-104	52	14	}	}	PUNCT
ma-104	52	15	.	.	PUNCT
ma-104	53	1	proof	proof	NOUN
ma-104	53	2	.	.	PUNCT
ma-104	54	1	the	the	DET
ma-104	54	2	result	result	NOUN
ma-104	54	3	follows	follow	VERB
ma-104	54	4	from	from	ADP
ma-104	54	5	definition	definition	NOUN
ma-104	54	6	of	of	ADP
ma-104	54	7	sequence	sequence	NOUN
ma-104	54	8	{	{	PUNCT
ma-104	54	9	sn	sn	NOUN
ma-104	54	10	}	}	PUNCT
ma-104	54	11	and	and	CCONJ
ma-104	54	12	hypothesis	hypothesis	NOUN
ma-104	54	13	(	(	PUNCT
ma-104	54	14	2.1	2.1	NUM
ma-104	54	15	)	)	PUNCT
ma-104	54	16	.	.	PUNCT
ma-104	55	1	�	�	PROPN
ma-104	55	2	let	let	VERB
ma-104	55	3	ε	ε	PROPN
ma-104	55	4	be	be	AUX
ma-104	55	5	a	a	DET
ma-104	55	6	positive	positive	ADJ
ma-104	55	7	constant	constant	NOUN
ma-104	55	8	.	.	PUNCT
ma-104	56	1	moreover	moreover	ADV
ma-104	56	2	,	,	PUNCT
ma-104	56	3	introduce	introduce	VERB
ma-104	56	4	parameters	parameter	NOUN
ma-104	56	5	by	by	ADP
ma-104	56	6	α	α	X
ma-104	56	7	=	=	SYM
ma-104	56	8	1+ε	1+ε	PROPN
ma-104	56	9	,	,	PUNCT
ma-104	56	10	β	β	X
ma-104	56	11	=	=	SYM
ma-104	56	12	l	l	NOUN
ma-104	56	13	(	(	PUNCT
ma-104	56	14	1+q)(1+ε	1+q)(1+ε	NUM
ma-104	56	15	)	)	PUNCT
ma-104	56	16	,	,	PUNCT
ma-104	56	17	γ	γ	PROPN
ma-104	56	18	=	=	SYM
ma-104	56	19	ε	ε	PROPN
ma-104	56	20	(	(	PUNCT
ma-104	56	21	1+ε)l0	1+ε)l0	NUM
ma-104	56	22	,	,	PUNCT
ma-104	56	23	δ	δ	PROPN
ma-104	56	24	=	=	PUNCT
ma-104	56	25	β(s2	β(s2	NOUN
ma-104	56	26	−	−	PROPN
ma-104	56	27	s1	s1	PROPN
ma-104	56	28	)	)	PUNCT
ma-104	56	29	,	,	PUNCT
ma-104	57	1	λ	λ	X
ma-104	57	2	=	=	SYM
ma-104	57	3	γ	γ	X
ma-104	57	4	1	1	NUM
ma-104	57	5	q	q	NOUN
ma-104	57	6	,	,	PUNCT
ma-104	57	7	h	h	NOUN
ma-104	57	8	=	=	PUNCT
ma-104	57	9	δ1+q	δ1+q	PROPN
ma-104	57	10	and	and	CCONJ
ma-104	57	11	u	u	NOUN
ma-104	57	12	=	=	PUNCT
ma-104	57	13	(	(	PUNCT
ma-104	57	14	1k0	1k0	NUM
ma-104	57	15	)	)	PUNCT
ma-104	57	16	1	1	NUM
ma-104	57	17	q	q	NOUN
ma-104	57	18	.	.	PUNCT
ma-104	58	1	furthermore	furthermore	ADV
ma-104	58	2	,	,	PUNCT
ma-104	58	3	consider	consider	VERB
ma-104	58	4	functions	function	NOUN
ma-104	58	5	withcommon	withcommon	ADJ
ma-104	58	6	domain	domain	NOUN
ma-104	58	7	in	in	ADP
ma-104	58	8	t	t	NOUN
ma-104	58	9	=	=	PUNCT
ma-104	59	1	[	[	X
ma-104	59	2	0	0	NUM
ma-104	59	3	,	,	PUNCT
ma-104	59	4	u	u	NOUN
ma-104	59	5	)	)	PUNCT
ma-104	59	6	given	give	VERB
ma-104	59	7	as	as	ADP
ma-104	59	8	https://doi.org/10.28924/ada/ma.3.5	https://doi.org/10.28924/ada/ma.3.5	PROPN
ma-104	59	9	eur	eur	PROPN
ma-104	59	10	.	.	PUNCT
ma-104	60	1	j.	j.	PROPN
ma-104	60	2	math	math	PROPN
ma-104	60	3	.	.	PUNCT
ma-104	61	1	anal	anal	PROPN
ma-104	61	2	.	.	PUNCT
ma-104	62	1	10.28924	10.28924	NUM
ma-104	62	2	/	/	SYM
ma-104	62	3	ada	ada	PROPN
ma-104	62	4	/	/	SYM
ma-104	62	5	ma.3.5	ma.3.5	PROPN
ma-104	62	6	3	3	NUM
ma-104	62	7	f1(t	f1(t	NUM
ma-104	62	8	)	)	PUNCT
ma-104	62	9	=	=	SYM
ma-104	62	10	(	(	PUNCT
ma-104	62	11	ktq	ktq	X
ma-104	62	12	(	(	PUNCT
ma-104	62	13	1	1	NUM
ma-104	62	14	+	+	CCONJ
ma-104	62	15	q)(1−k0tq	q)(1−k0tq	ADJ
ma-104	62	16	)	)	PUNCT
ma-104	62	17	+	+	NUM
ma-104	62	18	t	t	NOUN
ma-104	62	19	)	)	PUNCT
ma-104	62	20	q	q	NOUN
ma-104	62	21	−	−	PROPN
ma-104	62	22	γ	γ	X
ma-104	62	23	,	,	PUNCT
ma-104	62	24	f2(t	f2(t	PROPN
ma-104	62	25	)	)	PUNCT
ma-104	62	26	klαt1+q	klαt1+q	NOUN
ma-104	62	27	(	(	PUNCT
ma-104	62	28	1	1	NUM
ma-104	62	29	+	+	NUM
ma-104	62	30	q)2(1−k0tq	q)2(1−k0tq	NOUN
ma-104	62	31	)	)	PUNCT
ma-104	63	1	−	−	PROPN
ma-104	63	2	1	1	NUM
ma-104	63	3	and	and	CCONJ
ma-104	63	4	f3(t	f3(t	NUM
ma-104	63	5	)	)	PUNCT
ma-104	63	6	=	=	NOUN
ma-104	64	1	(	(	PUNCT
ma-104	64	2	s2	s2	NOUN
ma-104	64	3	+	+	CCONJ
ma-104	64	4	β−	β−	PROPN
ma-104	64	5	1	1	NUM
ma-104	64	6	q	q	NOUN
ma-104	64	7	h	h	NOUN
ma-104	64	8	1−	1−	NUM
ma-104	64	9	h	h	NOUN
ma-104	64	10	)	)	PUNCT
ma-104	64	11	q	q	NOUN
ma-104	65	1	−	−	PROPN
ma-104	65	2	γ	γ	X
ma-104	65	3	.	.	PUNCT
ma-104	66	1	it	it	PRON
ma-104	66	2	follows	follow	VERB
ma-104	66	3	by	by	ADP
ma-104	66	4	these	these	DET
ma-104	66	5	definitions	definition	NOUN
ma-104	66	6	f1(0	f1(0	PROPN
ma-104	66	7	)	)	PUNCT
ma-104	66	8	=	=	PUNCT
ma-104	67	1	−γ	−γ	ADP
ma-104	67	2	<	<	X
ma-104	67	3	0	0	NUM
ma-104	67	4	,	,	PUNCT
ma-104	67	5	f2(0	f2(0	NOUN
ma-104	67	6	)	)	PUNCT
ma-104	67	7	=	=	SYM
ma-104	67	8	−1	−1	NOUN
ma-104	67	9	<	<	X
ma-104	67	10	0	0	NUM
ma-104	67	11	,	,	PUNCT
ma-104	67	12	f3(0	f3(0	PROPN
ma-104	67	13	)	)	PUNCT
ma-104	68	1	=	=	VERB
ma-104	68	2	−γ	−γ	ADP
ma-104	68	3	<	<	X
ma-104	68	4	0	0	NUM
ma-104	68	5	and	and	CCONJ
ma-104	68	6	f1(t	f1(t	PROPN
ma-104	68	7	)	)	PUNCT
ma-104	68	8	−→	−→	NOUN
ma-104	68	9	∞	∞	PROPN
ma-104	68	10	,	,	PUNCT
ma-104	68	11	f2(t	f2(t	PROPN
ma-104	68	12	)	)	PUNCT
ma-104	68	13	−→	−→	NOUN
ma-104	68	14	∞	∞	PROPN
ma-104	68	15	and	and	CCONJ
ma-104	68	16	f3(t	f3(t	NUM
ma-104	68	17	)	)	PUNCT
ma-104	68	18	−→	−→	NOUN
ma-104	68	19	∞	∞	PROPN
ma-104	68	20	as	as	ADP
ma-104	68	21	t	t	PROPN
ma-104	68	22	−→	−→	NOUN
ma-104	68	23	u−.	u−.	ADJ
ma-104	68	24	so	so	ADV
ma-104	68	25	,	,	PUNCT
ma-104	68	26	function	function	NOUN
ma-104	68	27	fi	fi	NOUN
ma-104	68	28	,	,	PUNCT
ma-104	68	29	i	i	PRON
ma-104	68	30	=	=	NOUN
ma-104	68	31	1	1	NUM
ma-104	68	32	,	,	PUNCT
ma-104	68	33	2	2	NUM
ma-104	68	34	,	,	PUNCT
ma-104	68	35	3	3	NUM
ma-104	68	36	have	have	VERB
ma-104	68	37	zeros	zero	NOUN
ma-104	68	38	in	in	ADP
ma-104	68	39	interval	interval	NOUN
ma-104	68	40	t	t	PROPN
ma-104	68	41	by	by	ADP
ma-104	68	42	ivt	ivt	PROPN
ma-104	68	43	(	(	PUNCT
ma-104	68	44	intermediate	intermediate	ADJ
ma-104	68	45	value	value	NOUN
ma-104	68	46	theorem	theorem	NOUN
ma-104	68	47	)	)	PUNCT
ma-104	68	48	.	.	PUNCT
ma-104	69	1	let	let	VERB
ma-104	69	2	ηi	ηi	PROPN
ma-104	69	3	denote	denote	VERB
ma-104	69	4	the	the	DET
ma-104	69	5	smallest	small	ADJ
ma-104	69	6	such	such	ADJ
ma-104	69	7	zero	zero	NUM
ma-104	69	8	of	of	ADP
ma-104	69	9	functions	function	NOUN
ma-104	69	10	fi	fi	NOUN
ma-104	69	11	ininterval	ininterval	NOUN
ma-104	69	12	t0	t0	PROPN
ma-104	69	13	=	=	SYM
ma-104	69	14	(	(	PUNCT
ma-104	69	15	0	0	NUM
ma-104	69	16	,	,	PUNCT
ma-104	69	17	u	u	NOUN
ma-104	69	18	)	)	PUNCT
ma-104	69	19	,	,	PUNCT
ma-104	69	20	respectively.it	respectively.it	PRON
ma-104	69	21	also	also	ADV
ma-104	69	22	follows	follow	VERB
ma-104	69	23	by	by	ADP
ma-104	69	24	these	these	DET
ma-104	69	25	choices	choice	NOUN
ma-104	69	26	of	of	ADP
ma-104	69	27	zeros	zero	NOUN
ma-104	69	28	ηi	ηi	PROPN
ma-104	70	1	k0s	k0s	PROPN
ma-104	70	2	q	q	PROPN
ma-104	70	3	1	1	NUM
ma-104	70	4	<	<	SYM
ma-104	70	5	1	1	NUM
ma-104	70	6	,	,	PUNCT
ma-104	70	7	sq2	sq2	PROPN
ma-104	70	8	<	<	X
ma-104	70	9	γ	γ	PROPN
ma-104	70	10	,	,	PUNCT
ma-104	70	11	f1(t	f1(t	PROPN
ma-104	70	12	)	)	PUNCT
ma-104	70	13	<	<	X
ma-104	70	14	0	0	PUNCT
ma-104	70	15	at	at	ADP
ma-104	70	16	t	t	NOUN
ma-104	70	17	=	=	SYM
ma-104	70	18	η1	η1	NOUN
ma-104	70	19	(	(	PUNCT
ma-104	70	20	2.3	2.3	NUM
ma-104	70	21	)	)	PUNCT
ma-104	70	22	δ	δ	PROPN
ma-104	70	23	<	<	X
ma-104	70	24	1	1	NUM
ma-104	70	25	,	,	PUNCT
ma-104	70	26	f2(t	f2(t	PROPN
ma-104	70	27	)	)	PUNCT
ma-104	70	28	<	<	X
ma-104	70	29	0	0	PUNCT
ma-104	71	1	at	at	ADP
ma-104	71	2	t	t	NOUN
ma-104	71	3	=	=	SYM
ma-104	71	4	η2	η2	PROPN
ma-104	71	5	(	(	PUNCT
ma-104	71	6	2.4	2.4	NUM
ma-104	71	7	)	)	PUNCT
ma-104	71	8	and	and	CCONJ
ma-104	71	9	f3(t	f3(t	NOUN
ma-104	71	10	)	)	PUNCT
ma-104	71	11	<	<	X
ma-104	71	12	0	0	PUNCT
ma-104	72	1	at	at	ADP
ma-104	72	2	t	t	NOUN
ma-104	72	3	=	=	SYM
ma-104	72	4	η3	η3	PROPN
ma-104	72	5	.	.	PUNCT
ma-104	73	1	(	(	PUNCT
ma-104	73	2	2.5	2.5	NUM
ma-104	73	3	)	)	PUNCT
ma-104	73	4	define	define	VERB
ma-104	73	5	parameter	parameter	NOUN
ma-104	73	6	η0	η0	NOUN
ma-104	73	7	=	=	SYM
ma-104	73	8	min{ηi	min{ηi	X
ma-104	73	9	}	}	PUNCT
ma-104	73	10	.	.	PUNCT
ma-104	74	1	(	(	PUNCT
ma-104	74	2	2.6	2.6	NUM
ma-104	74	3	)	)	PUNCT
ma-104	74	4	suppose	suppose	VERB
ma-104	74	5	η	η	PROPN
ma-104	74	6	≤	≤	PROPN
ma-104	74	7	η0	η0	NOUN
ma-104	74	8	.	.	PUNCT
ma-104	75	1	(	(	PUNCT
ma-104	75	2	2.7	2.7	NUM
ma-104	75	3	)	)	PUNCT
ma-104	75	4	if	if	SCONJ
ma-104	75	5	η0	η0	NOUN
ma-104	75	6	=	=	SYM
ma-104	75	7	η1	η1	NOUN
ma-104	75	8	or	or	CCONJ
ma-104	75	9	η0	η0	NOUN
ma-104	75	10	=	=	SYM
ma-104	75	11	η2	η2	NOUN
ma-104	75	12	,	,	PUNCT
ma-104	75	13	suppose	suppose	VERB
ma-104	75	14	hypothesis	hypothesis	NOUN
ma-104	75	15	(	(	PUNCT
ma-104	75	16	2.7	2.7	NUM
ma-104	75	17	)	)	PUNCT
ma-104	75	18	holds	hold	VERB
ma-104	75	19	as	as	SCONJ
ma-104	75	20	a	a	DET
ma-104	75	21	strict	strict	ADJ
ma-104	75	22	inequality.a	inequality.a	PROPN
ma-104	75	23	second	second	ADV
ma-104	75	24	stronger	strong	ADJ
ma-104	75	25	convergence	convergence	NOUN
ma-104	75	26	result	result	NOUN
ma-104	75	27	follows	follow	VERB
ma-104	75	28	.	.	PUNCT
ma-104	76	1	but	but	CCONJ
ma-104	76	2	hypotheses	hypothesis	NOUN
ma-104	76	3	are	be	AUX
ma-104	76	4	easier	easy	ADJ
ma-104	76	5	to	to	PART
ma-104	76	6	verify	verify	VERB
ma-104	76	7	.	.	PUNCT
ma-104	77	1	lemma	lemma	PROPN
ma-104	77	2	2.2	2.2	NUM
ma-104	77	3	.	.	PUNCT
ma-104	78	1	suppose	suppose	VERB
ma-104	78	2	hypothesis	hypothesis	NOUN
ma-104	78	3	(	(	PUNCT
ma-104	78	4	2.7	2.7	NUM
ma-104	78	5	)	)	PUNCT
ma-104	78	6	holds	hold	VERB
ma-104	78	7	.	.	PUNCT
ma-104	79	1	then	then	ADV
ma-104	79	2	,	,	PUNCT
ma-104	79	3	sequence	sequence	NOUN
ma-104	79	4	{	{	PUNCT
ma-104	79	5	sn	sn	NOUN
ma-104	79	6	}	}	PUNCT
ma-104	79	7	is	be	AUX
ma-104	79	8	strictly	strictly	ADV
ma-104	79	9	increasing	increase	VERB
ma-104	79	10	and	and	CCONJ
ma-104	79	11	convergent	convergent	NOUN
ma-104	79	12	to	to	ADP
ma-104	79	13	some	some	DET
ma-104	79	14	s∗	s∗	PROPN
ma-104	79	15	∈	∈	PROPN
ma-104	79	16	(	(	PUNCT
ma-104	79	17	0	0	NUM
ma-104	79	18	,	,	PUNCT
ma-104	79	19	γ0	γ0	NOUN
ma-104	79	20	)	)	PUNCT
ma-104	79	21	,	,	PUNCT
ma-104	79	22	where	where	SCONJ
ma-104	79	23	γ0	γ0	NOUN
ma-104	79	24	=	=	SYM
ma-104	79	25	s2	s2	PROPN
ma-104	79	26	+	+	CCONJ
ma-104	79	27	β	β	X
ma-104	79	28	−	−	NOUN
ma-104	79	29	1q	1q	NUM
ma-104	79	30	h	h	NOUN
ma-104	79	31	1−h	1−h	NUM
ma-104	79	32	.	.	PUNCT
ma-104	80	1	moreover	moreover	ADV
ma-104	80	2	,	,	PUNCT
ma-104	80	3	for	for	ADP
ma-104	80	4	σn+2	σn+2	NUM
ma-104	80	5	=	=	SYM
ma-104	80	6	sn+2	sn+2	PROPN
ma-104	80	7	−	−	NOUN
ma-104	80	8	sn+1	sn+1	X
ma-104	80	9	∀n	∀n	PUNCT
ma-104	80	10	=	=	SYM
ma-104	80	11	0	0	NUM
ma-104	80	12	,	,	PUNCT
ma-104	80	13	1	1	NUM
ma-104	80	14	,	,	PUNCT
ma-104	80	15	2	2	NUM
ma-104	80	16	,	,	PUNCT
ma-104	80	17	.	.	PUNCT
ma-104	80	18	.	.	PUNCT
ma-104	80	19	.	.	PUNCT
ma-104	81	1	σn+2	σn+2	NUM
ma-104	81	2	≤	≤	NUM
ma-104	81	3	βσ1+qn+1	βσ1+qn+1	PUNCT
ma-104	81	4	≤	≤	NOUN
ma-104	81	5	β	β	X
ma-104	81	6	−	−	PROPN
ma-104	81	7	1	1	NUM
ma-104	81	8	q	q	NOUN
ma-104	81	9	δ(1	δ(1	PROPN
ma-104	81	10	+	+	NOUN
ma-104	81	11	)	)	PUNCT
ma-104	81	12	n	n	CCONJ
ma-104	81	13	(	(	PUNCT
ma-104	81	14	2.8	2.8	NUM
ma-104	81	15	)	)	PUNCT
ma-104	81	16	and	and	CCONJ
ma-104	81	17	s∗	s∗	PROPN
ma-104	81	18	−	−	PROPN
ma-104	81	19	sn+1	sn+1	VERB
ma-104	81	20	≤	≤	NUM
ma-104	81	21	β−	β−	NOUN
ma-104	81	22	1	1	NUM
ma-104	81	23	q	q	NOUN
ma-104	81	24	δ(1+q	δ(1+q	PROPN
ma-104	81	25	)	)	PUNCT
ma-104	81	26	n	n	PROPN
ma-104	81	27	1−	1−	NUM
ma-104	81	28	δ1+q	δ1+q	PROPN
ma-104	81	29	.	.	PUNCT
ma-104	82	1	(	(	PUNCT
ma-104	82	2	2.9	2.9	NUM
ma-104	82	3	)	)	PUNCT
ma-104	82	4	proof	proof	NOUN
ma-104	82	5	.	.	PUNCT
ma-104	83	1	the	the	DET
ma-104	83	2	assertions	assertion	NOUN
ma-104	83	3	(	(	PUNCT
ma-104	83	4	ij	ij	NOUN
ma-104	83	5	)	)	PUNCT
ma-104	83	6	:	:	PUNCT
ma-104	83	7	0	0	PUNCT
ma-104	83	8	<	<	X
ma-104	83	9	1	1	NUM
ma-104	83	10	1−	1−	NUM
ma-104	83	11	l0sqj+1	l0sqj+1	NOUN
ma-104	83	12	≤	≤	NUM
ma-104	83	13	α	α	PRON
ma-104	83	14	(	(	PUNCT
ma-104	83	15	2.10	2.10	NUM
ma-104	83	16	)	)	PUNCT
ma-104	83	17	https://doi.org/10.28924/ada/ma.3.5	https://doi.org/10.28924/ada/ma.3.5	PROPN
ma-104	83	18	eur	eur	PROPN
ma-104	83	19	.	.	PUNCT
ma-104	84	1	j.	j.	PROPN
ma-104	84	2	math	math	PROPN
ma-104	84	3	.	.	PUNCT
ma-104	85	1	anal	anal	PROPN
ma-104	85	2	.	.	PUNCT
ma-104	86	1	10.28924	10.28924	NUM
ma-104	86	2	/	/	SYM
ma-104	86	3	ada	ada	PROPN
ma-104	86	4	/	/	SYM
ma-104	86	5	ma.3.5	ma.3.5	PROPN
ma-104	86	6	4is	4is	NOUN
ma-104	86	7	shown	show	VERB
ma-104	86	8	using	use	VERB
ma-104	86	9	induction	induction	NOUN
ma-104	86	10	.	.	PUNCT
ma-104	87	1	assertion	assertion	NOUN
ma-104	87	2	(	(	PUNCT
ma-104	87	3	i1	i1	PROPN
ma-104	87	4	)	)	PUNCT
ma-104	87	5	is	be	AUX
ma-104	87	6	true	true	ADJ
ma-104	87	7	by	by	ADP
ma-104	87	8	the	the	DET
ma-104	87	9	choice	choice	NOUN
ma-104	87	10	of	of	ADP
ma-104	87	11	η1	η1	NOUN
ma-104	87	12	and	and	CCONJ
ma-104	87	13	estimates	estimate	NOUN
ma-104	87	14	(	(	PUNCT
ma-104	87	15	2.3	2.3	NUM
ma-104	87	16	)	)	PUNCT
ma-104	87	17	.	.	PUNCT
ma-104	88	1	it	it	PRON
ma-104	88	2	followsby	followsby	VERB
ma-104	88	3	(	(	PUNCT
ma-104	88	4	i1	i1	PROPN
ma-104	88	5	)	)	PUNCT
ma-104	88	6	and	and	CCONJ
ma-104	88	7	sequence	sequence	NOUN
ma-104	88	8	{	{	PUNCT
ma-104	88	9	sn	sn	NOUN
ma-104	88	10	}	}	PUNCT
ma-104	88	11	that	that	SCONJ
ma-104	88	12	0	0	PUNCT
ma-104	88	13	<	<	X
ma-104	88	14	s3	s3	PROPN
ma-104	88	15	−	−	PROPN
ma-104	88	16	s2	s2	PROPN
ma-104	88	17	≤	≤	PUNCT
ma-104	88	18	β(s2	β(s2	NOUN
ma-104	89	1	−	−	PROPN
ma-104	89	2	s1)1+q	s1)1+q	PROPN
ma-104	89	3	,	,	PUNCT
ma-104	89	4	or	or	CCONJ
ma-104	89	5	s3	s3	PROPN
ma-104	89	6	<	<	X
ma-104	89	7	s2	s2	PROPN
ma-104	89	8	+	+	CCONJ
ma-104	89	9	β−	β−	PROPN
ma-104	89	10	1	1	NUM
ma-104	89	11	q	q	NOUN
ma-104	89	12	δ(1+q	δ(1+q	NOUN
ma-104	89	13	)	)	PUNCT
ma-104	89	14	1	1	NUM
ma-104	89	15	≤	≤	NUM
ma-104	89	16	γ.so	γ.so	VERB
ma-104	89	17	,	,	PUNCT
ma-104	89	18	assertion	assertion	NOUN
ma-104	89	19	(	(	PUNCT
ma-104	89	20	2.8	2.8	NUM
ma-104	89	21	)	)	PUNCT
ma-104	89	22	holds	hold	VERB
ma-104	89	23	for	for	ADP
ma-104	89	24	n	n	NOUN
ma-104	89	25	=	=	SYM
ma-104	89	26	1	1	X
ma-104	89	27	.	.	PUNCT
ma-104	89	28	suppose	suppose	VERB
ma-104	89	29	assertion	assertion	NOUN
ma-104	89	30	(	(	PUNCT
ma-104	89	31	2.10	2.10	NUM
ma-104	89	32	)	)	PUNCT
ma-104	89	33	holds	hold	VERB
ma-104	89	34	∀j	∀j	NOUN
ma-104	89	35	=	=	SYM
ma-104	89	36	1	1	NUM
ma-104	89	37	,	,	PUNCT
ma-104	89	38	2	2	NUM
ma-104	89	39	,	,	PUNCT
ma-104	89	40	.	.	PUNCT
ma-104	89	41	.	.	PUNCT
ma-104	89	42	.	.	PUNCT
ma-104	90	1	n.	n.	PROPN
ma-104	90	2	then	then	ADV
ma-104	90	3	,	,	PUNCT
ma-104	90	4	0	0	PUNCT
ma-104	90	5	<	<	X
ma-104	90	6	σn+1	σn+1	PROPN
ma-104	90	7	≤	≤	NOUN
ma-104	90	8	βσ1+qnand	βσ1+qnand	PUNCT
ma-104	90	9	sn+1	sn+1	NUM
ma-104	90	10	≤	≤	NUM
ma-104	90	11	sn	sn	PROPN
ma-104	91	1	+	+	X
ma-104	91	2	βσ1+qn	βσ1+qn	PROPN
ma-104	91	3	≤	≤	NUM
ma-104	91	4	.	.	PUNCT
ma-104	91	5	.	.	PUNCT
ma-104	91	6	.	.	PUNCT
ma-104	92	1	≤	≤	NUM
ma-104	92	2	s2	s2	NOUN
ma-104	92	3	+	+	CCONJ
ma-104	92	4	β	β	X
ma-104	92	5	(	(	PUNCT
ma-104	92	6	1+q)−1	1+q)−1	NUM
ma-104	92	7	1+q−1	1+q−1	NUM
ma-104	92	8	σ1+q2	σ1+q2	PROPN
ma-104	93	1	+	+	NUM
ma-104	93	2	β	β	X
ma-104	93	3	(	(	PUNCT
ma-104	93	4	1+q)2−1	1+q)2−1	NUM
ma-104	93	5	1+q−1	1+q−1	PROPN
ma-104	93	6	σ	σ	NOUN
ma-104	93	7	(	(	PUNCT
ma-104	93	8	1+q)2	1+q)2	NUM
ma-104	93	9	2	2	NUM
ma-104	93	10	+	+	CCONJ
ma-104	93	11	.	.	PUNCT
ma-104	93	12	.	.	PUNCT
ma-104	94	1	.+	.+	NOUN
ma-104	94	2	β	β	X
ma-104	94	3	(	(	PUNCT
ma-104	94	4	1+q)n−1−1	1+q)n−1−1	PROPN
ma-104	94	5	1+q−1	1+q−1	PROPN
ma-104	94	6	σ	σ	NOUN
ma-104	94	7	(	(	PUNCT
ma-104	94	8	1+q)n−1	1+q)n−1	NUM
ma-104	94	9	2	2	NUM
ma-104	94	10	=	=	NOUN
ma-104	94	11	s2	s2	NOUN
ma-104	94	12	+	+	CCONJ
ma-104	94	13	β−	β−	PROPN
ma-104	94	14	1	1	NUM
ma-104	94	15	q	q	NOUN
ma-104	94	16	(	(	PUNCT
ma-104	94	17	δ1+q	δ1+q	PROPN
ma-104	94	18	+	+	NOUN
ma-104	94	19	δ2(1+q	δ2(1+q	NOUN
ma-104	94	20	)	)	PUNCT
ma-104	94	21	+	+	CCONJ
ma-104	94	22	.	.	PUNCT
ma-104	94	23	.	.	PUNCT
ma-104	95	1	.+	.+	NOUN
ma-104	95	2	δ(n−1)(1+q	δ(n−1)(1+q	PROPN
ma-104	95	3	)	)	PUNCT
ma-104	95	4	)	)	PUNCT
ma-104	96	1	(	(	PUNCT
ma-104	96	2	δ	δ	X
ma-104	96	3	<	<	X
ma-104	96	4	1	1	NUM
ma-104	96	5	)	)	PUNCT
ma-104	96	6	=	=	SYM
ma-104	96	7	s2	s2	NOUN
ma-104	96	8	+	+	CCONJ
ma-104	96	9	β−	β−	PROPN
ma-104	96	10	1	1	NUM
ma-104	96	11	q	q	NOUN
ma-104	96	12	δ1+q	δ1+q	PROPN
ma-104	96	13	1−	1−	NUM
ma-104	96	14	(	(	PUNCT
ma-104	96	15	δ1+q)n−1	δ1+q)n−1	NOUN
ma-104	96	16	1−	1−	NUM
ma-104	96	17	δ1+q	δ1+q	PROPN
ma-104	96	18	<	<	X
ma-104	96	19	s2	s2	NOUN
ma-104	96	20	+	+	CCONJ
ma-104	96	21	β−	β−	NUM
ma-104	96	22	1	1	NUM
ma-104	96	23	q	q	NOUN
ma-104	96	24	δ1+q	δ1+q	PROPN
ma-104	96	25	1−	1−	NUM
ma-104	96	26	δ1+q	δ1+q	PROPN
ma-104	96	27	=	=	PROPN
ma-104	96	28	s2	s2	PROPN
ma-104	96	29	+	+	CCONJ
ma-104	96	30	β−	β−	PROPN
ma-104	96	31	1	1	NUM
ma-104	96	32	q	q	NOUN
ma-104	96	33	h	h	NOUN
ma-104	96	34	1−	1−	NUM
ma-104	96	35	h	h	NOUN
ma-104	96	36	=	=	SYM
ma-104	96	37	γ0	γ0	PROPN
ma-104	96	38	.	.	PUNCT
ma-104	97	1	hence	hence	ADV
ma-104	97	2	,	,	PUNCT
ma-104	97	3	estimate	estimate	VERB
ma-104	97	4	sqn+1	sqn+1	VERB
ma-104	97	5	≤	≤	NUM
ma-104	97	6	γholds	γhold	NOUN
ma-104	97	7	if	if	SCONJ
ma-104	97	8	f3(t	f3(t	NOUN
ma-104	97	9	)	)	PUNCT
ma-104	97	10	≤	≤	NOUN
ma-104	97	11	0	0	NUM
ma-104	98	1	at	at	ADP
ma-104	98	2	t	t	NOUN
ma-104	98	3	=	=	SYM
ma-104	98	4	η3	η3	PROPN
ma-104	98	5	,	,	PUNCT
ma-104	98	6	which	which	PRON
ma-104	98	7	is	be	AUX
ma-104	98	8	estimate	estimate	NOUN
ma-104	98	9	(	(	PUNCT
ma-104	98	10	2.5	2.5	NUM
ma-104	98	11	)	)	PUNCT
ma-104	98	12	.	.	PUNCT
ma-104	99	1	the	the	DET
ma-104	99	2	induction	induction	NOUN
ma-104	99	3	for	for	ADP
ma-104	99	4	assertion	assertion	NOUN
ma-104	99	5	(	(	PUNCT
ma-104	99	6	2.10	2.10	NUM
ma-104	99	7	)	)	PUNCT
ma-104	99	8	is	be	AUX
ma-104	99	9	completed.it	completed.it	NOUN
ma-104	99	10	follows	follow	VERB
ma-104	99	11	that	that	DET
ma-104	99	12	estimate	estimate	NOUN
ma-104	99	13	(	(	PUNCT
ma-104	99	14	2.8	2.8	NUM
ma-104	99	15	)	)	PUNCT
ma-104	99	16	holds	hold	VERB
ma-104	99	17	.	.	PUNCT
ma-104	100	1	notice	notice	NOUN
ma-104	100	2	δ	δ	PROPN
ma-104	100	3	=	=	PUNCT
ma-104	100	4	βσ2	βσ2	PROPN
ma-104	101	1	=	=	SYM
ma-104	101	2	lα	lα	ADP
ma-104	101	3	1	1	NUM
ma-104	101	4	+	+	NOUN
ma-104	101	5	q	q	PROPN
ma-104	101	6	kσ1+q1	kσ1+q1	NOUN
ma-104	101	7	(	(	PUNCT
ma-104	101	8	1	1	NUM
ma-104	101	9	+	+	NUM
ma-104	101	10	q)(1−k0sq1	q)(1−k0sq1	NUM
ma-104	101	11	)	)	PUNCT
ma-104	101	12	<	<	X
ma-104	101	13	1	1	NUM
ma-104	101	14	(	(	PUNCT
ma-104	101	15	2.11	2.11	NUM
ma-104	101	16	)	)	PUNCT
ma-104	101	17	also	also	ADV
ma-104	101	18	holds	hold	VERB
ma-104	101	19	since	since	SCONJ
ma-104	101	20	it	it	PRON
ma-104	101	21	is	be	AUX
ma-104	101	22	equivalent	equivalent	ADJ
ma-104	101	23	to	to	ADP
ma-104	101	24	the	the	DET
ma-104	101	25	second	second	ADJ
ma-104	101	26	estimate	estimate	NOUN
ma-104	101	27	in	in	ADP
ma-104	101	28	(	(	PUNCT
ma-104	101	29	2.4	2.4	NUM
ma-104	101	30	)	)	PUNCT
ma-104	101	31	.	.	PUNCT
ma-104	102	1	let	let	VERB
ma-104	102	2	n	n	NOUN
ma-104	102	3	=	=	SYM
ma-104	102	4	2	2	NUM
ma-104	102	5	,	,	PUNCT
ma-104	102	6	3	3	NUM
ma-104	102	7	,	,	PUNCT
ma-104	102	8	.	.	PUNCT
ma-104	102	9	.	.	PUNCT
ma-104	102	10	.	.	PUNCT
ma-104	102	11	.	.	PUNCT
ma-104	103	1	then	then	ADV
ma-104	103	2	,	,	PUNCT
ma-104	103	3	it	it	PRON
ma-104	103	4	followsin	followsin	VERB
ma-104	103	5	turn	turn	VERB
ma-104	103	6	by	by	ADP
ma-104	103	7	assertion	assertion	NOUN
ma-104	103	8	(	(	PUNCT
ma-104	103	9	2.8	2.8	NUM
ma-104	103	10	)	)	PUNCT
ma-104	103	11	sj+n	sj+n	NOUN
ma-104	103	12	−	−	NOUN
ma-104	103	13	sj+1	sj+1	PROPN
ma-104	103	14	≤	≤	PROPN
ma-104	103	15	σj+n	σj+n	PROPN
ma-104	103	16	+	+	CCONJ
ma-104	103	17	σj+n−1	σj+n−1	PROPN
ma-104	103	18	+	+	CCONJ
ma-104	103	19	.	.	PUNCT
ma-104	103	20	.	.	PUNCT
ma-104	104	1	.+	.+	NOUN
ma-104	104	2	σj+2	σj+2	NOUN
ma-104	104	3	≤	≤	NUM
ma-104	104	4	β−	β−	NOUN
ma-104	104	5	1	1	NUM
ma-104	104	6	q	q	NOUN
ma-104	104	7	(	(	PUNCT
ma-104	104	8	δ(1+q	δ(1+q	PROPN
ma-104	104	9	)	)	PUNCT
ma-104	104	10	j+n−2	j+n−2	ADP
ma-104	104	11	+	+	PUNCT
ma-104	104	12	δ(1+q	δ(1+q	PROPN
ma-104	104	13	)	)	PUNCT
ma-104	104	14	j+n−1	j+n−1	PROPN
ma-104	105	1	+	+	CCONJ
ma-104	105	2	.	.	PUNCT
ma-104	105	3	.	.	PUNCT
ma-104	106	1	.+	.+	NOUN
ma-104	106	2	δ(1+q	δ(1+q	PROPN
ma-104	106	3	)	)	PUNCT
ma-104	106	4	j	j	PROPN
ma-104	106	5	)	)	PUNCT
ma-104	106	6	≤	≤	PUNCT
ma-104	107	1	β−	β−	PUNCT
ma-104	107	2	1	1	NUM
ma-104	107	3	q	q	NOUN
ma-104	107	4	δ(1+q	δ(1+q	PROPN
ma-104	107	5	)	)	PUNCT
ma-104	107	6	n	n	CCONJ
ma-104	107	7	δ1+q	δ1+q	PROPN
ma-104	107	8	1−	1−	NUM
ma-104	107	9	δ2n−1	δ2n−1	PROPN
ma-104	107	10	1−	1−	NUM
ma-104	107	11	δ1+q	δ1+q	PROPN
ma-104	107	12	.	.	PUNCT
ma-104	108	1	(	(	PUNCT
ma-104	108	2	2.12	2.12	NUM
ma-104	108	3	)	)	PUNCT
ma-104	108	4	then	then	ADV
ma-104	108	5	,	,	PUNCT
ma-104	108	6	assertion	assertion	NOUN
ma-104	108	7	(	(	PUNCT
ma-104	108	8	2.9	2.9	NUM
ma-104	108	9	)	)	PUNCT
ma-104	108	10	follows	follow	VERB
ma-104	108	11	from	from	ADP
ma-104	108	12	estimate	estimate	NOUN
ma-104	108	13	(	(	PUNCT
ma-104	108	14	2.12	2.12	NUM
ma-104	108	15	)	)	PUNCT
ma-104	108	16	if	if	SCONJ
ma-104	108	17	n	n	NUM
ma-104	108	18	−→∞.	−→∞.	X
ma-104	108	19	�	�	PROPN
ma-104	108	20	remark	remark	VERB
ma-104	108	21	2.3	2.3	NUM
ma-104	108	22	.	.	PUNCT
ma-104	109	1	an	an	DET
ma-104	109	2	at	at	ADV
ma-104	109	3	least	least	ADJ
ma-104	109	4	as	as	ADP
ma-104	109	5	large	large	ADJ
ma-104	109	6	parameter	parameter	NOUN
ma-104	109	7	as	as	SCONJ
ma-104	109	8	η3	η3	PROPN
ma-104	109	9	can	can	AUX
ma-104	109	10	replace	replace	VERB
ma-104	109	11	it	it	PRON
ma-104	109	12	in	in	ADP
ma-104	109	13	condition	condition	NOUN
ma-104	109	14	(	(	PUNCT
ma-104	109	15	2.7	2.7	NUM
ma-104	109	16	)	)	PUNCT
ma-104	109	17	as	as	SCONJ
ma-104	109	18	follows	follow	VERB
ma-104	109	19	.	.	PUNCT
ma-104	110	1	define	define	VERB
ma-104	110	2	sequences	sequence	NOUN
ma-104	110	3	of	of	ADP
ma-104	110	4	functions	function	NOUN
ma-104	110	5	ϕn	ϕn	X
ma-104	110	6	on	on	ADP
ma-104	110	7	the	the	DET
ma-104	110	8	interval	interval	NOUN
ma-104	110	9	t	t	NOUN
ma-104	110	10	by	by	ADP
ma-104	110	11	ϕn(t	ϕn(t	NOUN
ma-104	110	12	)	)	PUNCT
ma-104	111	1	=	=	PRON
ma-104	111	2	(	(	PUNCT
ma-104	111	3	s2(t	s2(t	PROPN
ma-104	111	4	)	)	PUNCT
ma-104	112	1	+	+	CCONJ
ma-104	112	2	β−	β−	PROPN
ma-104	112	3	1	1	NUM
ma-104	112	4	q	q	NOUN
ma-104	112	5	(	(	PUNCT
ma-104	112	6	δ(t)1+q	δ(t)1+q	NOUN
ma-104	112	7	+	+	CCONJ
ma-104	112	8	δ(t)(1+q	δ(t)(1+q	NOUN
ma-104	112	9	)	)	PUNCT
ma-104	112	10	2	2	NUM
ma-104	112	11	+	+	CCONJ
ma-104	112	12	.	.	PUNCT
ma-104	112	13	.	.	PUNCT
ma-104	113	1	.+	.+	NOUN
ma-104	113	2	δ(t)(1+q	δ(t)(1+q	PROPN
ma-104	113	3	)	)	PUNCT
ma-104	113	4	n−1	n−1	PROPN
ma-104	113	5	)	)	PUNCT
ma-104	113	6	q	q	NOUN
ma-104	113	7	−	−	PROPN
ma-104	113	8	γ	γ	X
ma-104	113	9	.	.	PUNCT
ma-104	114	1	(	(	PUNCT
ma-104	114	2	2.13	2.13	NUM
ma-104	114	3	)	)	PUNCT
ma-104	114	4	https://doi.org/10.28924/ada/ma.3.5	https://doi.org/10.28924/ada/ma.3.5	PROPN
ma-104	114	5	eur	eur	PROPN
ma-104	114	6	.	.	PUNCT
ma-104	115	1	j.	j.	PROPN
ma-104	115	2	math	math	PROPN
ma-104	115	3	.	.	PUNCT
ma-104	116	1	anal	anal	PROPN
ma-104	116	2	.	.	PUNCT
ma-104	117	1	10.28924	10.28924	NUM
ma-104	117	2	/	/	SYM
ma-104	117	3	ada	ada	PROPN
ma-104	117	4	/	/	SYM
ma-104	117	5	ma.3.5	ma.3.5	NOUN
ma-104	117	6	5	5	NUM
ma-104	117	7	it	it	PRON
ma-104	117	8	follows	follow	VERB
ma-104	117	9	by	by	ADP
ma-104	117	10	these	these	DET
ma-104	117	11	definition	definition	NOUN
ma-104	118	1	that	that	SCONJ
ma-104	118	2	ϕn+1(t)−	ϕn+1(t)−	PROPN
ma-104	118	3	ϕn(t	ϕn(t	PRON
ma-104	118	4	)	)	PUNCT
ma-104	118	5	≥	≥	NOUN
ma-104	118	6	0	0	NUM
ma-104	118	7	,	,	PUNCT
ma-104	118	8	so	so	ADV
ma-104	118	9	ϕn(t	ϕn(t	PUNCT
ma-104	118	10	)	)	PUNCT
ma-104	118	11	≤	≤	NUM
ma-104	118	12	ϕn+1(t	ϕn+1(t	CCONJ
ma-104	118	13	)	)	PUNCT
ma-104	119	1	∀t	∀t	PROPN
ma-104	119	2	∈	∈	PROPN
ma-104	119	3	t.	t.	NOUN
ma-104	119	4	(	(	PUNCT
ma-104	119	5	2.14	2.14	NUM
ma-104	119	6	)	)	PUNCT
ma-104	119	7	moreover	moreover	ADP
ma-104	119	8	these	these	DET
ma-104	119	9	functions	function	NOUN
ma-104	119	10	have	have	VERB
ma-104	119	11	zeros	zero	NOUN
ma-104	119	12	in	in	ADP
ma-104	119	13	t0	t0	NOUN
ma-104	119	14	.	.	PUNCT
ma-104	120	1	these	these	DET
ma-104	120	2	zeros	zero	NOUN
ma-104	120	3	are	be	AUX
ma-104	120	4	assured	assure	VERB
ma-104	120	5	to	to	PART
ma-104	120	6	exist	exist	VERB
ma-104	120	7	by	by	ADP
ma-104	120	8	(	(	PUNCT
ma-104	120	9	ivt	ivt	PROPN
ma-104	120	10	)	)	PUNCT
ma-104	120	11	,	,	PUNCT
ma-104	120	12	since	since	SCONJ
ma-104	120	13	by	by	ADP
ma-104	120	14	the	the	DET
ma-104	120	15	definitions	definition	NOUN
ma-104	120	16	of	of	ADP
ma-104	120	17	fucntions	fucntion	NOUN
ma-104	120	18	ϕn	ϕn	AUX
ma-104	120	19	give	give	VERB
ma-104	120	20	ϕn(0	ϕn(0	PRON
ma-104	120	21	)	)	PUNCT
ma-104	120	22	=	=	PUNCT
ma-104	121	1	−γ	−γ	ADP
ma-104	121	2	<	<	X
ma-104	121	3	0	0	NUM
ma-104	121	4	and	and	CCONJ
ma-104	121	5	ϕn(t	ϕn(t	NUM
ma-104	121	6	)	)	PUNCT
ma-104	121	7	−→	−→	NOUN
ma-104	121	8	∞	∞	PROPN
ma-104	121	9	as	as	SCONJ
ma-104	121	10	t	t	PROPN
ma-104	121	11	−→	−→	NOUN
ma-104	121	12	u−.	u−.	PROPN
ma-104	121	13	denote	denote	NOUN
ma-104	121	14	the	the	DET
ma-104	121	15	smallest	small	ADJ
ma-104	121	16	such	such	ADJ
ma-104	121	17	zeros	zero	NOUN
ma-104	121	18	of	of	ADP
ma-104	121	19	functions	function	NOUN
ma-104	121	20	ϕn	ϕn	VERB
ma-104	121	21	in	in	ADP
ma-104	121	22	t	t	PROPN
ma-104	121	23	by	by	ADP
ma-104	121	24	rn	rn	PROPN
ma-104	121	25	,	,	PUNCT
ma-104	121	26	respectively	respectively	ADV
ma-104	121	27	.	.	PUNCT
ma-104	122	1	according	accord	VERB
ma-104	122	2	to	to	ADP
ma-104	122	3	the	the	DET
ma-104	122	4	proof	proof	NOUN
ma-104	122	5	of	of	ADP
ma-104	122	6	lemma	lemma	PROPN
ma-104	122	7	2.2	2.2	NUM
ma-104	122	8	,	,	PUNCT
ma-104	122	9	lim	lim	PROPN
ma-104	122	10	n−→∞	n−→∞	PROPN
ma-104	122	11	ϕn(t	ϕn(t	PRON
ma-104	122	12	)	)	PUNCT
ma-104	122	13	≤	≤	PUNCT
ma-104	123	1	f3(t	f3(t	X
ma-104	123	2	)	)	PUNCT
ma-104	123	3	∀t	∀t	PROPN
ma-104	123	4	∈	∈	PROPN
ma-104	123	5	t.	t.	NOUN
ma-104	123	6	(	(	PUNCT
ma-104	123	7	2.15	2.15	NUM
ma-104	123	8	)	)	PUNCT
ma-104	123	9	so	so	ADV
ma-104	123	10	,	,	PUNCT
ma-104	123	11	this	this	DET
ma-104	123	12	limit	limit	NOUN
ma-104	123	13	exists	exist	VERB
ma-104	123	14	as	as	ADP
ma-104	123	15	a	a	DET
ma-104	123	16	well	well	ADV
ma-104	123	17	defined	define	VERB
ma-104	123	18	function	function	NOUN
ma-104	123	19	denoted	denote	VERB
ma-104	123	20	by	by	ADP
ma-104	123	21	ψ	ψ	X
ma-104	123	22	.	.	PUNCT
ma-104	124	1	then	then	ADV
ma-104	124	2	,	,	PUNCT
ma-104	124	3	this	this	DET
ma-104	124	4	function	function	NOUN
ma-104	124	5	has	have	VERB
ma-104	124	6	zeros	zero	NOUN
ma-104	124	7	in	in	ADP
ma-104	124	8	t0	t0	PROPN
ma-104	124	9	,	,	PUNCT
ma-104	124	10	since	since	SCONJ
ma-104	124	11	ψ(0	ψ(0	NOUN
ma-104	124	12	)	)	PUNCT
ma-104	124	13	=	=	VERB
ma-104	124	14	−γ	−γ	NOUN
ma-104	124	15	and	and	CCONJ
ma-104	124	16	ψ(t	ψ(t	PROPN
ma-104	124	17	)	)	PUNCT
ma-104	125	1	−→	−→	NOUN
ma-104	125	2	∞	∞	PROPN
ma-104	125	3	as	as	ADP
ma-104	125	4	t	t	PROPN
ma-104	125	5	−→	−→	NOUN
ma-104	125	6	u−.	u−.	ADJ
ma-104	125	7	denote	denote	NOUN
ma-104	125	8	by	by	ADP
ma-104	125	9	η4	η4	VERB
ma-104	125	10	the	the	DET
ma-104	125	11	smallest	small	ADJ
ma-104	125	12	such	such	ADJ
ma-104	125	13	zero	zero	NUM
ma-104	125	14	in	in	ADP
ma-104	125	15	(	(	PUNCT
ma-104	125	16	0	0	NUM
ma-104	125	17	,	,	PUNCT
ma-104	125	18	u	u	NOUN
ma-104	125	19	)	)	PUNCT
ma-104	125	20	.	.	PUNCT
ma-104	126	1	clearly	clearly	ADV
ma-104	126	2	,	,	PUNCT
ma-104	126	3	the	the	DET
ma-104	126	4	proof	proof	NOUN
ma-104	126	5	of	of	ADP
ma-104	126	6	lemma	lemma	PROPN
ma-104	126	7	2.2	2.2	NUM
ma-104	126	8	goes	go	VERB
ma-104	126	9	through	through	ADP
ma-104	126	10	if	if	SCONJ
ma-104	126	11	instead	instead	ADV
ma-104	126	12	of	of	ADP
ma-104	126	13	f3(t	f3(t	NOUN
ma-104	126	14	)	)	PUNCT
ma-104	126	15	≤	≤	NOUN
ma-104	126	16	0	0	NUM
ma-104	126	17	,	,	PUNCT
ma-104	126	18	it	it	PRON
ma-104	126	19	is	be	AUX
ma-104	126	20	shown	show	VERB
ma-104	126	21	that	that	SCONJ
ma-104	126	22	ψ3(t	ψ3(t	PROPN
ma-104	126	23	)	)	PUNCT
ma-104	126	24	≤	≤	NOUN
ma-104	126	25	0	0	NUM
ma-104	126	26	∀t	∀t	PROPN
ma-104	126	27	∈	∈	PROPN
ma-104	126	28	t.	t.	NOUN
ma-104	126	29	(	(	PUNCT
ma-104	126	30	2.16	2.16	NUM
ma-104	126	31	)	)	PUNCT
ma-104	126	32	define	define	VERB
ma-104	126	33	parameter	parameter	NOUN
ma-104	126	34	η̄0	η̄0	NOUN
ma-104	126	35	=	=	PUNCT
ma-104	126	36	min{η1	min{η1	NOUN
ma-104	126	37	,	,	PUNCT
ma-104	126	38	η2	η2	NOUN
ma-104	126	39	,	,	PUNCT
ma-104	126	40	η4	η4	VERB
ma-104	126	41	}	}	PUNCT
ma-104	126	42	.	.	PUNCT
ma-104	127	1	notice	notice	VERB
ma-104	127	2	that	that	SCONJ
ma-104	127	3	by	by	ADP
ma-104	127	4	(	(	PUNCT
ma-104	127	5	2.15	2.15	NUM
ma-104	127	6	)	)	PUNCT
ma-104	127	7	ψ(η3	ψ(η3	NOUN
ma-104	127	8	)	)	PUNCT
ma-104	127	9	≤	≤	NUM
ma-104	127	10	f3(η3	f3(η3	NOUN
ma-104	127	11	)	)	PUNCT
ma-104	127	12	=	=	SYM
ma-104	127	13	0	0	NUM
ma-104	127	14	,	,	PUNCT
ma-104	127	15	so	so	ADV
ma-104	127	16	η3	η3	PROPN
ma-104	127	17	≤	≤	NOUN
ma-104	127	18	η4	η4	VERB
ma-104	127	19	and	and	CCONJ
ma-104	127	20	consequenlty	consequenlty	NOUN
ma-104	127	21	η0	η0	NOUN
ma-104	127	22	≤	≤	NOUN
ma-104	127	23	η̄0	η̄0	NOUN
ma-104	127	24	.	.	PUNCT
ma-104	128	1	if	if	SCONJ
ma-104	128	2	η̄0	η̄0	NOUN
ma-104	128	3	replaces	replace	VERB
ma-104	128	4	η0	η0	NOUN
ma-104	128	5	in	in	ADP
ma-104	128	6	condition	condition	NOUN
ma-104	128	7	(	(	PUNCT
ma-104	128	8	2.6	2.6	NUM
ma-104	128	9	)	)	PUNCT
ma-104	128	10	,	,	PUNCT
ma-104	128	11	then	then	ADV
ma-104	128	12	assertion	assertion	NOUN
ma-104	128	13	(	(	PUNCT
ma-104	128	14	2.16	2.16	NUM
ma-104	128	15	)	)	PUNCT
ma-104	128	16	follows	follow	VERB
ma-104	128	17	.	.	PUNCT
ma-104	129	1	condition	condition	NOUN
ma-104	129	2	(	(	PUNCT
ma-104	129	3	2.7	2.7	NUM
ma-104	129	4	)	)	PUNCT
ma-104	129	5	becomes	become	VERB
ma-104	129	6	η	η	PROPN
ma-104	129	7	≤	≤	NOUN
ma-104	129	8	η̄0	η̄0	NOUN
ma-104	129	9	.	.	PUNCT
ma-104	130	1	(	(	PUNCT
ma-104	130	2	2.17	2.17	NUM
ma-104	130	3	)	)	PUNCT
ma-104	130	4	hence	hence	ADV
ma-104	130	5	,	,	PUNCT
ma-104	130	6	the	the	DET
ma-104	130	7	range	range	NOUN
ma-104	130	8	of	of	ADP
ma-104	130	9	initial	initial	ADJ
ma-104	130	10	approximations	approximation	NOUN
ma-104	130	11	η	η	NOUN
ma-104	130	12	is	be	AUX
ma-104	130	13	further	far	ADV
ma-104	130	14	extended	extend	VERB
ma-104	130	15	.	.	PUNCT
ma-104	131	1	3	3	X
ma-104	131	2	.	.	X
ma-104	131	3	convergence	convergence	NOUN
ma-104	131	4	of	of	ADP
ma-104	131	5	nm	nm	DET
ma-104	131	6	the	the	DET
ma-104	131	7	notation	notation	NOUN
ma-104	131	8	u(w	u(w	PROPN
ma-104	131	9	,	,	PUNCT
ma-104	131	10	ρ	ρ	PROPN
ma-104	131	11	)	)	PUNCT
ma-104	131	12	,	,	PUNCT
ma-104	131	13	u[w	u[w	PROPN
ma-104	131	14	,	,	PUNCT
ma-104	131	15	ρ	ρ	PROPN
ma-104	131	16	]	]	PUNCT
ma-104	131	17	means	mean	VERB
ma-104	131	18	the	the	DET
ma-104	131	19	open	open	ADJ
ma-104	131	20	and	and	CCONJ
ma-104	131	21	closed	closed	ADJ
ma-104	131	22	balls	ball	NOUN
ma-104	131	23	with	with	ADP
ma-104	131	24	radius	radius	NOUN
ma-104	131	25	ρ	ρ	PROPN
ma-104	131	26	>	>	X
ma-104	131	27	0	0	PUNCT
ma-104	132	1	and	and	CCONJ
ma-104	132	2	center	center	PROPN
ma-104	132	3	w	w	PROPN
ma-104	132	4	∈	∈	PROPN
ma-104	132	5	x	x	X
ma-104	132	6	,	,	PUNCT
ma-104	132	7	respectively	respectively	ADV
ma-104	132	8	.	.	PUNCT
ma-104	133	1	the	the	DET
ma-104	133	2	parameters	parameter	NOUN
ma-104	133	3	k0	k0	PROPN
ma-104	133	4	,	,	PUNCT
ma-104	133	5	l0	l0	PROPN
ma-104	133	6	,	,	PUNCT
ma-104	133	7	k	k	NOUN
ma-104	133	8	,	,	PUNCT
ma-104	133	9	l	l	PROPN
ma-104	133	10	and	and	CCONJ
ma-104	133	11	t	t	PROPN
ma-104	133	12	are	be	AUX
ma-104	133	13	connected	connect	VERB
ma-104	133	14	with	with	ADP
ma-104	133	15	operator	operator	NOUN
ma-104	133	16	f	f	PROPN
ma-104	133	17	as	as	ADP
ma-104	133	18	follows.consider	follows.consider	PROPN
ma-104	133	19	conditions	condition	NOUN
ma-104	133	20	(	(	PUNCT
ma-104	133	21	a):suppose(a1	a):suppose(a1	VERB
ma-104	133	22	)	)	PUNCT
ma-104	133	23	there	there	ADV
ma-104	133	24	exist	exist	VERB
ma-104	134	1	x0	x0	PROPN
ma-104	134	2	∈	∈	PROPN
ma-104	134	3	ω	ω	PROPN
ma-104	134	4	,	,	PUNCT
ma-104	134	5	t	t	PROPN
ma-104	134	6	≥	≥	NUM
ma-104	134	7	0	0	NUM
ma-104	134	8	such	such	ADJ
ma-104	134	9	that	that	SCONJ
ma-104	134	10	f	f	PROPN
ma-104	134	11	′(x0)−1	′(x0)−1	PROPN
ma-104	134	12	∈	∈	PROPN
ma-104	134	13	l(m2,m1	l(m2,m1	PROPN
ma-104	134	14	)	)	PUNCT
ma-104	134	15	,	,	PUNCT
ma-104	134	16	‖f	‖f	PRON
ma-104	134	17	′(x0)−1f	′(x0)−1f	NOUN
ma-104	134	18	(	(	PUNCT
ma-104	134	19	x0)‖	x0)‖	PROPN
ma-104	134	20	≤	≤	ADJ
ma-104	134	21	t.	t.	NOUN
ma-104	134	22	‖f	‖f	ADJ
ma-104	134	23	′(x0)−1(f	′(x0)−1(f	PROPN
ma-104	134	24	′(x1)−	′(x1)−	PROPN
ma-104	134	25	f	f	X
ma-104	134	26	′(x0))‖	′(x0))‖	NUM
ma-104	134	27	≤	≤	NUM
ma-104	134	28	k0‖x1	k0‖x1	PROPN
ma-104	134	29	−	−	PROPN
ma-104	134	30	x0‖qand	x0‖qand	NOUN
ma-104	134	31	‖f	‖f	PUNCT
ma-104	135	1	′(x0)−1(f	′(x0)−1(f	PROPN
ma-104	135	2	′(x0	′(x0	NOUN
ma-104	135	3	+	+	CCONJ
ma-104	135	4	τ(x1	τ(x1	NUM
ma-104	136	1	−	−	PROPN
ma-104	137	1	x0))−	x0))−	PROPN
ma-104	138	1	f	f	PROPN
ma-104	139	1	′(x0))‖	′(x0))‖	NUM
ma-104	139	2	≤	≤	PROPN
ma-104	139	3	k‖τ(x1	k‖τ(x1	PROPN
ma-104	139	4	−	−	PROPN
ma-104	139	5	x0)‖q.(a2	x0)‖q.(a2	PROPN
ma-104	139	6	)	)	PUNCT
ma-104	139	7	‖f	‖f	PUNCT
ma-104	140	1	′(x0)−1(f	′(x0)−1(f	PROPN
ma-104	140	2	′(x)−	′(x)−	PROPN
ma-104	140	3	f	f	PROPN
ma-104	140	4	′(x0))‖	′(x0))‖	NUM
ma-104	140	5	≤	≤	NUM
ma-104	140	6	l0‖x	l0‖x	NUM
ma-104	140	7	−	−	NOUN
ma-104	140	8	x0‖q	x0‖q	PROPN
ma-104	140	9	,	,	PUNCT
ma-104	140	10	∀x	∀x	X
ma-104	140	11	∈	∈	PROPN
ma-104	140	12	ω	ω	X
ma-104	140	13	.	.	PUNCT
ma-104	141	1	set	set	VERB
ma-104	141	2	b1	b1	NOUN
ma-104	141	3	=	=	SYM
ma-104	141	4	u(x0	u(x0	NOUN
ma-104	141	5	,	,	PUNCT
ma-104	141	6	(	(	PUNCT
ma-104	141	7	1l0	1l0	NUM
ma-104	141	8	)	)	PUNCT
ma-104	141	9	1	1	NUM
ma-104	141	10	q	q	NOUN
ma-104	141	11	)	)	PUNCT
ma-104	141	12	∩ω.(a3	∩ω.(a3	PROPN
ma-104	141	13	)	)	PUNCT
ma-104	141	14	‖f	‖f	PUNCT
ma-104	141	15	′(x0)−1(f	′(x0)−1(f	VERB
ma-104	141	16	′(x	′(x	NOUN
ma-104	141	17	+	+	CCONJ
ma-104	141	18	τ(y	τ(y	PROPN
ma-104	142	1	−	−	NOUN
ma-104	142	2	x))−	x))−	NOUN
ma-104	142	3	f	f	PROPN
ma-104	142	4	′(x))‖	′(x))‖	PROPN
ma-104	142	5	≤	≤	NOUN
ma-104	142	6	l‖τ(y	l‖τ(y	NOUN
ma-104	142	7	−	−	PROPN
ma-104	142	8	x)‖q	x)‖q	PROPN
ma-104	142	9	∀x	∀x	NUM
ma-104	142	10	,	,	PUNCT
ma-104	142	11	y	y	PROPN
ma-104	142	12	∈	∈	PROPN
ma-104	142	13	b1	b1	NOUN
ma-104	142	14	and	and	CCONJ
ma-104	142	15	∀τ	∀τ	NOUN
ma-104	142	16	∈	∈	PROPN
ma-104	143	1	[	[	X
ma-104	143	2	0	0	NUM
ma-104	143	3	,	,	PUNCT
ma-104	143	4	1).(a4	1).(a4	NUM
ma-104	143	5	)	)	PUNCT
ma-104	143	6	conditions	condition	NOUN
ma-104	143	7	of	of	ADP
ma-104	143	8	lemma	lemma	PROPN
ma-104	143	9	2.1	2.1	NUM
ma-104	143	10	or	or	CCONJ
ma-104	143	11	lemma	lemma	PROPN
ma-104	143	12	2.2	2.2	NUM
ma-104	143	13	hold(a5	hold(a5	NOUN
ma-104	143	14	)	)	PUNCT
ma-104	143	15	u[x0	u[x0	NOUN
ma-104	143	16	,	,	PUNCT
ma-104	143	17	t	t	PROPN
ma-104	143	18	∗	∗	NOUN
ma-104	143	19	]	]	PUNCT
ma-104	144	1	⊂	⊂	PROPN
ma-104	144	2	ω	ω	PROPN
ma-104	144	3	.	.	PUNCT
ma-104	145	1	https://doi.org/10.28924/ada/ma.3.5	https://doi.org/10.28924/ada/ma.3.5	PROPN
ma-104	145	2	eur	eur	PROPN
ma-104	145	3	.	.	PUNCT
ma-104	146	1	j.	j.	PROPN
ma-104	146	2	math	math	PROPN
ma-104	146	3	.	.	PUNCT
ma-104	147	1	anal	anal	PROPN
ma-104	147	2	.	.	PUNCT
ma-104	148	1	10.28924	10.28924	NUM
ma-104	148	2	/	/	SYM
ma-104	148	3	ada	ada	PROPN
ma-104	148	4	/	/	SYM
ma-104	148	5	ma.3.5	ma.3.5	PROPN
ma-104	148	6	6notice	6notice	NUM
ma-104	148	7	that	that	PRON
ma-104	148	8	k0	k0	PROPN
ma-104	148	9	≤	≤	PROPN
ma-104	148	10	k	k	PROPN
ma-104	148	11	≤	≤	PROPN
ma-104	148	12	l0.next	l0.next	NOUN
ma-104	148	13	,	,	PUNCT
ma-104	148	14	conditions	condition	NOUN
ma-104	148	15	a	a	PRON
ma-104	148	16	are	be	AUX
ma-104	148	17	applied	apply	VERB
ma-104	148	18	to	to	PART
ma-104	148	19	show	show	VERB
ma-104	148	20	the	the	DET
ma-104	148	21	main	main	ADJ
ma-104	148	22	convergence	convergence	NOUN
ma-104	148	23	result	result	NOUN
ma-104	148	24	for	for	ADP
ma-104	148	25	ni	ni	PROPN
ma-104	148	26	.	.	PROPN
ma-104	148	27	theorem	theorem	VERB
ma-104	148	28	3.1	3.1	NUM
ma-104	148	29	.	.	PUNCT
ma-104	149	1	under	under	ADP
ma-104	149	2	conditions	condition	NOUN
ma-104	149	3	a	a	DET
ma-104	149	4	sequence	sequence	NOUN
ma-104	149	5	ni	ni	PROPN
ma-104	149	6	is	be	AUX
ma-104	149	7	convergent	convergent	ADJ
ma-104	149	8	to	to	ADP
ma-104	149	9	a	a	DET
ma-104	149	10	solution	solution	NOUN
ma-104	149	11	x∗	x∗	PROPN
ma-104	149	12	∈	∈	PROPN
ma-104	149	13	u[x0	u[x0	NOUN
ma-104	149	14	,	,	PUNCT
ma-104	149	15	s	s	PART
ma-104	149	16	∗	∗	NOUN
ma-104	149	17	]	]	PUNCT
ma-104	149	18	of	of	ADP
ma-104	149	19	equation	equation	NOUN
ma-104	149	20	f	f	PROPN
ma-104	149	21	(	(	PUNCT
ma-104	149	22	x∗	x∗	X
ma-104	149	23	)	)	PUNCT
ma-104	149	24	=	=	SYM
ma-104	150	1	0	0	X
ma-104	150	2	.	.	PUNCT
ma-104	151	1	moreover	moreover	ADV
ma-104	151	2	,	,	PUNCT
ma-104	151	3	upper	upper	ADJ
ma-104	151	4	bounds	bound	NOUN
ma-104	151	5	‖x∗	‖x∗	PUNCT
ma-104	152	1	−	−	NOUN
ma-104	152	2	xn‖	xn‖	PROPN
ma-104	152	3	≤	≤	PROPN
ma-104	152	4	s∗	s∗	AUX
ma-104	152	5	−	−	PROPN
ma-104	152	6	sn	sn	PROPN
ma-104	152	7	(	(	PUNCT
ma-104	152	8	3.1	3.1	NUM
ma-104	152	9	)	)	PUNCT
ma-104	152	10	hold	hold	VERB
ma-104	152	11	∀n	∀n	NOUN
ma-104	152	12	=	=	SYM
ma-104	152	13	0	0	NUM
ma-104	152	14	,	,	PUNCT
ma-104	152	15	1	1	NUM
ma-104	152	16	,	,	PUNCT
ma-104	152	17	2	2	NUM
ma-104	152	18	,	,	PUNCT
ma-104	152	19	.	.	PUNCT
ma-104	152	20	.	.	PUNCT
ma-104	152	21	.	.	PUNCT
ma-104	152	22	.	.	PUNCT
ma-104	153	1	proof	proof	NOUN
ma-104	153	2	.	.	PUNCT
ma-104	154	1	the	the	DET
ma-104	154	2	items	item	NOUN
ma-104	154	3	‖xi+1	‖xi+1	ADP
ma-104	154	4	−	−	PROPN
ma-104	154	5	xi‖	xi‖	PROPN
ma-104	154	6	≤	≤	NOUN
ma-104	154	7	si+1	si+1	PROPN
ma-104	154	8	−	−	NOUN
ma-104	154	9	si	si	INTJ
ma-104	154	10	,	,	PUNCT
ma-104	154	11	(	(	PUNCT
ma-104	154	12	3.2)and	3.2)and	NUM
ma-104	154	13	u[xi+1	u[xi+1	NOUN
ma-104	154	14	,	,	PUNCT
ma-104	154	15	s	s	NOUN
ma-104	154	16	∗	∗	NOUN
ma-104	154	17	−	−	NOUN
ma-104	154	18	si+1	si+1	NOUN
ma-104	154	19	]	]	X
ma-104	154	20	⊆	⊆	NUM
ma-104	154	21	u[xi	u[xi	NOUN
ma-104	154	22	,	,	PUNCT
ma-104	154	23	s	s	NOUN
ma-104	154	24	∗	∗	NOUN
ma-104	154	25	−	−	NOUN
ma-104	154	26	si	si	X
ma-104	154	27	]	]	X
ma-104	154	28	,	,	PUNCT
ma-104	154	29	(	(	PUNCT
ma-104	154	30	3.3)are	3.3)are	NUM
ma-104	154	31	shown	show	VERB
ma-104	154	32	by	by	ADP
ma-104	154	33	induction	induction	NOUN
ma-104	154	34	∀i	∀i	NOUN
ma-104	154	35	=	=	SYM
ma-104	154	36	0	0	NUM
ma-104	154	37	,	,	PUNCT
ma-104	154	38	1	1	NUM
ma-104	154	39	,	,	PUNCT
ma-104	154	40	2	2	NUM
ma-104	154	41	,	,	PUNCT
ma-104	154	42	.	.	PUNCT
ma-104	154	43	.	.	PUNCT
ma-104	154	44	.	.	PUNCT
ma-104	155	1	.	.	PUNCT
ma-104	156	1	let	let	VERB
ma-104	156	2	u	u	PRON
ma-104	156	3	∈	∈	PRON
ma-104	156	4	u[x1	u[x1	VERB
ma-104	156	5	,	,	PUNCT
ma-104	156	6	s	s	NOUN
ma-104	156	7	∗	∗	NOUN
ma-104	156	8	−	−	NOUN
ma-104	156	9	s1	s1	NOUN
ma-104	156	10	]	]	PUNCT
ma-104	156	11	.	.	PUNCT
ma-104	157	1	it	it	PRON
ma-104	157	2	follows	follow	VERB
ma-104	157	3	by	by	ADP
ma-104	157	4	condition	condition	NOUN
ma-104	157	5	(	(	PUNCT
ma-104	157	6	a1	a1	NOUN
ma-104	157	7	)	)	PUNCT
ma-104	157	8	‖x1	‖x1	NOUN
ma-104	157	9	−	−	PROPN
ma-104	157	10	x0‖	x0‖	PROPN
ma-104	158	1	=	=	PUNCT
ma-104	158	2	‖f	‖f	DET
ma-104	158	3	′(x0)−1f	′(x0)−1f	NOUN
ma-104	158	4	(	(	PUNCT
ma-104	158	5	x0)‖	x0)‖	PROPN
ma-104	158	6	≤	≤	X
ma-104	158	7	t	t	NOUN
ma-104	158	8	=	=	SYM
ma-104	158	9	s1	s1	PROPN
ma-104	158	10	−	−	PROPN
ma-104	158	11	s0	s0	PROPN
ma-104	158	12	,	,	PUNCT
ma-104	158	13	‖u	‖u	PROPN
ma-104	158	14	−	−	PROPN
ma-104	158	15	x0‖	x0‖	PROPN
ma-104	158	16	≤	≤	PROPN
ma-104	158	17	‖u	‖u	NOUN
ma-104	158	18	−	−	PROPN
ma-104	159	1	x1‖+	x1‖+	PUNCT
ma-104	160	1	‖x1	‖x1	NOUN
ma-104	160	2	−	−	PROPN
ma-104	160	3	x0‖	x0‖	PROPN
ma-104	160	4	≤	≤	PROPN
ma-104	160	5	s∗	s∗	VERB
ma-104	160	6	−	−	PROPN
ma-104	160	7	s1	s1	PROPN
ma-104	160	8	+	+	CCONJ
ma-104	160	9	s1	s1	PROPN
ma-104	160	10	−	−	PROPN
ma-104	160	11	s0	s0	NOUN
ma-104	160	12	=	=	SYM
ma-104	160	13	s∗.hence	s∗.hence	PROPN
ma-104	160	14	,	,	PUNCT
ma-104	160	15	point	point	VERB
ma-104	160	16	u	u	NOUN
ma-104	160	17	∈	∈	PROPN
ma-104	160	18	u[x0	u[x0	NOUN
ma-104	160	19	,	,	PUNCT
ma-104	160	20	s	s	PART
ma-104	160	21	∗−s0	∗−s0	NOUN
ma-104	160	22	]	]	PUNCT
ma-104	160	23	.	.	PUNCT
ma-104	161	1	that	that	PRON
ma-104	161	2	is	be	AUX
ma-104	161	3	items	item	NOUN
ma-104	161	4	(	(	PUNCT
ma-104	161	5	3.2	3.2	NUM
ma-104	161	6	)	)	PUNCT
ma-104	161	7	and	and	CCONJ
ma-104	161	8	(	(	PUNCT
ma-104	161	9	3.3	3.3	NUM
ma-104	161	10	)	)	PUNCT
ma-104	161	11	hold	hold	VERB
ma-104	161	12	for	for	ADP
ma-104	161	13	i	i	PRON
ma-104	161	14	=	=	NOUN
ma-104	161	15	0	0	X
ma-104	161	16	.	.	PUNCT
ma-104	162	1	assume	assume	VERB
ma-104	162	2	these	these	DET
ma-104	162	3	assertionshold	assertionshold	NOUN
ma-104	162	4	if	if	SCONJ
ma-104	162	5	i	i	PRON
ma-104	162	6	=	=	NOUN
ma-104	162	7	0	0	NUM
ma-104	162	8	,	,	PUNCT
ma-104	162	9	1	1	NUM
ma-104	162	10	,	,	PUNCT
ma-104	162	11	.	.	PUNCT
ma-104	162	12	.	.	PUNCT
ma-104	163	1	.	.	PUNCT
ma-104	164	1	,	,	PUNCT
ma-104	164	2	n.	n.	PROPN
ma-104	164	3	it	it	PRON
ma-104	164	4	follows	follow	VERB
ma-104	164	5	for	for	ADP
ma-104	164	6	each	each	DET
ma-104	164	7	ξ	ξ	PROPN
ma-104	164	8	∈	∈	PROPN
ma-104	165	1	[	[	X
ma-104	165	2	0	0	NUM
ma-104	165	3	,	,	PUNCT
ma-104	165	4	1	1	NUM
ma-104	165	5	]	]	PUNCT
ma-104	165	6	‖xi	‖xi	NUM
ma-104	166	1	+	+	NUM
ma-104	166	2	ξ(xi+1	ξ(xi+1	ADJ
ma-104	166	3	−	−	NOUN
ma-104	166	4	xi)−	xi)−	PROPN
ma-104	167	1	x0‖	x0‖	PROPN
ma-104	167	2	≤	≤	PROPN
ma-104	167	3	si	si	PROPN
ma-104	168	1	+	+	CCONJ
ma-104	168	2	ξ(si+1	ξ(si+1	PROPN
ma-104	168	3	−	−	PROPN
ma-104	168	4	si	si	NOUN
ma-104	168	5	)	)	PUNCT
ma-104	168	6	≤	≤	NOUN
ma-104	168	7	s∗	s∗	PROPN
ma-104	168	8	,	,	PUNCT
ma-104	168	9	and	and	CCONJ
ma-104	168	10	‖xi+1	‖xi+1	ADP
ma-104	168	11	−	−	PROPN
ma-104	168	12	xi‖	xi‖	PROPN
ma-104	168	13	≤	≤	NOUN
ma-104	169	1	i+1∑	i+1∑	PROPN
ma-104	169	2	j=1	j=1	NOUN
ma-104	169	3	‖xj	‖xj	NUM
ma-104	169	4	−	−	PROPN
ma-104	169	5	xj−1‖	xj−1‖	PROPN
ma-104	169	6	≤	≤	PUNCT
ma-104	170	1	i+1∑	i+1∑	PROPN
ma-104	170	2	j=1	j=1	NOUN
ma-104	170	3	(	(	PUNCT
ma-104	170	4	sj	sj	INTJ
ma-104	170	5	−	−	PROPN
ma-104	170	6	sj−1	sj−1	NOUN
ma-104	170	7	)	)	PUNCT
ma-104	170	8	=	=	SYM
ma-104	170	9	si+1	si+1	X
ma-104	170	10	.	.	PUNCT
ma-104	171	1	it	it	PRON
ma-104	171	2	follows	follow	VERB
ma-104	171	3	by	by	ADP
ma-104	171	4	induction	induction	NOUN
ma-104	171	5	hypotheses	hypothesis	NOUN
ma-104	171	6	,	,	PUNCT
ma-104	171	7	lemmas	lemma	NOUN
ma-104	171	8	and	and	CCONJ
ma-104	171	9	conditions	condition	NOUN
ma-104	171	10	(	(	PUNCT
ma-104	171	11	a1	a1	NOUN
ma-104	171	12	)	)	PUNCT
ma-104	171	13	and	and	CCONJ
ma-104	171	14	(	(	PUNCT
ma-104	171	15	a2	a2	PROPN
ma-104	171	16	)	)	PUNCT
ma-104	171	17	‖f	‖f	PUNCT
ma-104	172	1	′(x0)−1(f	′(x0)−1(f	PROPN
ma-104	172	2	′(xi+1)−	′(xi+1)−	NOUN
ma-104	172	3	f	f	PROPN
ma-104	172	4	′(x0))‖	′(x0))‖	NUM
ma-104	172	5	≤	≤	NUM
ma-104	172	6	k̄‖xi+1	k̄‖xi+1	PROPN
ma-104	172	7	−	−	PROPN
ma-104	173	1	x0‖q	x0‖q	PROPN
ma-104	173	2	,	,	PUNCT
ma-104	173	3	≤	≤	NUM
ma-104	173	4	k̄(si+1	k̄(si+1	PROPN
ma-104	173	5	−	−	PROPN
ma-104	173	6	s0)q	s0)q	PROPN
ma-104	173	7	≤	≤	PROPN
ma-104	173	8	k̄sqi+1	k̄sqi+1	NOUN
ma-104	173	9	<	<	X
ma-104	173	10	1	1	NUM
ma-104	173	11	.	.	PUNCT
ma-104	174	1	hence	hence	ADV
ma-104	174	2	,	,	PUNCT
ma-104	174	3	the	the	DET
ma-104	174	4	inverse	inverse	NOUN
ma-104	174	5	of	of	ADP
ma-104	174	6	linear	linear	ADJ
ma-104	174	7	operator	operator	NOUN
ma-104	174	8	f	f	PROPN
ma-104	174	9	′(xi+1	′(xi+1	PROPN
ma-104	174	10	)	)	PUNCT
ma-104	174	11	exists	exist	VERB
ma-104	174	12	.	.	PUNCT
ma-104	175	1	therefore	therefore	ADV
ma-104	175	2	,	,	PUNCT
ma-104	175	3	hence	hence	ADV
ma-104	175	4	,	,	PUNCT
ma-104	175	5	f	f	PROPN
ma-104	175	6	′(v)−1	′(v)−1	PROPN
ma-104	175	7	∈	∈	PROPN
ma-104	175	8	l(m2,m1	l(m2,m1	PROPN
ma-104	175	9	)	)	PUNCT
ma-104	175	10	and	and	CCONJ
ma-104	175	11	‖f	‖f	ADJ
ma-104	175	12	′(xi+1)−1f	′(xi+1)−1f	NOUN
ma-104	176	1	′(x0)‖	′(x0)‖	NOUN
ma-104	176	2	≤	≤	NUM
ma-104	176	3	1	1	NUM
ma-104	176	4	1−	1−	NUM
ma-104	176	5	k̄sqi+1	k̄sqi+1	NUM
ma-104	176	6	)	)	PUNCT
ma-104	176	7	,	,	PUNCT
ma-104	176	8	(	(	PUNCT
ma-104	176	9	3.4	3.4	NUM
ma-104	176	10	)	)	PUNCT
ma-104	176	11	follows	follow	VERB
ma-104	176	12	as	as	ADP
ma-104	176	13	a	a	DET
ma-104	176	14	consequence	consequence	NOUN
ma-104	176	15	of	of	ADP
ma-104	176	16	a	a	DET
ma-104	176	17	lemma	lemma	PROPN
ma-104	176	18	on	on	ADP
ma-104	176	19	invertible	invertible	ADJ
ma-104	176	20	linear	linear	PROPN
ma-104	176	21	operators	operator	NOUN
ma-104	176	22	due	due	ADP
ma-104	176	23	to	to	ADP
ma-104	176	24	banach	banach	NOUN
ma-104	176	25	[	[	X
ma-104	176	26	2	2	NUM
ma-104	176	27	,	,	PUNCT
ma-104	176	28	7	7	NUM
ma-104	176	29	]	]	PUNCT
ma-104	176	30	,	,	PUNCT
ma-104	176	31	where	where	SCONJ
ma-104	176	32	k̄	k̄	ADV
ma-104	176	33	=	=	X
ma-104	176	34	{	{	PUNCT
ma-104	176	35	k0	k0	PROPN
ma-104	176	36	,	,	PUNCT
ma-104	176	37	i	i	PROPN
ma-104	176	38	=	=	SYM
ma-104	176	39	0	0	NUM
ma-104	176	40	l0	l0	PROPN
ma-104	176	41	,	,	PUNCT
ma-104	176	42	i	i	PRON
ma-104	176	43	=	=	NOUN
ma-104	176	44	1	1	NUM
ma-104	176	45	,	,	PUNCT
ma-104	176	46	2	2	NUM
ma-104	176	47	,	,	PUNCT
ma-104	176	48	.	.	PUNCT
ma-104	176	49	.	.	PUNCT
ma-104	176	50	.	.	PUNCT
ma-104	177	1	.ni	.ni	PROPN
ma-104	177	2	gives	give	VERB
ma-104	177	3	https://doi.org/10.28924/ada/ma.3.5	https://doi.org/10.28924/ada/ma.3.5	PROPN
ma-104	177	4	eur	eur	NOUN
ma-104	177	5	.	.	PUNCT
ma-104	178	1	j.	j.	PROPN
ma-104	178	2	math	math	PROPN
ma-104	178	3	.	.	PUNCT
ma-104	179	1	anal	anal	PROPN
ma-104	179	2	.	.	PUNCT
ma-104	180	1	10.28924	10.28924	NUM
ma-104	180	2	/	/	SYM
ma-104	180	3	ada	ada	PROPN
ma-104	180	4	/	/	SYM
ma-104	180	5	ma.3.5	ma.3.5	PROPN
ma-104	180	6	7	7	NUM
ma-104	180	7	f	f	PROPN
ma-104	180	8	(	(	PUNCT
ma-104	180	9	xi+1	xi+1	NOUN
ma-104	180	10	)	)	PUNCT
ma-104	180	11	=	=	SYM
ma-104	181	1	f	f	X
ma-104	181	2	(	(	PUNCT
ma-104	181	3	xi+1)−	xi+1)−	PROPN
ma-104	181	4	f	f	PROPN
ma-104	181	5	(	(	PUNCT
ma-104	181	6	xi)−	xi)−	PROPN
ma-104	181	7	f	f	PROPN
ma-104	182	1	′(xi)(xi+1	′(xi)(xi+1	PUNCT
ma-104	183	1	−	−	PROPN
ma-104	183	2	xi	xi	NOUN
ma-104	183	3	)	)	PUNCT
ma-104	183	4	,	,	PUNCT
ma-104	184	1	=	=	SYM
ma-104	184	2	∫	∫	PROPN
ma-104	184	3	1	1	NUM
ma-104	184	4	0	0	NUM
ma-104	184	5	(	(	PUNCT
ma-104	184	6	f	f	X
ma-104	184	7	′(xi	′(xi	PROPN
ma-104	185	1	+	+	CCONJ
ma-104	185	2	ξ(xi+1	ξ(xi+1	ADJ
ma-104	185	3	−	−	PROPN
ma-104	185	4	xi))dξ	xi))dξ	PROPN
ma-104	186	1	−	−	PROPN
ma-104	186	2	f	f	SYM
ma-104	186	3	′(xi))(xi+1	′(xi))(xi+1	NUM
ma-104	186	4	−	−	NOUN
ma-104	186	5	xi	xi	PROPN
ma-104	186	6	)	)	PUNCT
ma-104	186	7	.	.	PUNCT
ma-104	187	1	(	(	PUNCT
ma-104	187	2	3.5	3.5	NUM
ma-104	187	3	)	)	PUNCT
ma-104	187	4	then	then	ADV
ma-104	187	5	,	,	PUNCT
ma-104	187	6	using	use	VERB
ma-104	187	7	induction	induction	NOUN
ma-104	187	8	hypotheses	hypothesis	NOUN
ma-104	187	9	,	,	PUNCT
ma-104	187	10	identity	identity	NOUN
ma-104	187	11	(	(	PUNCT
ma-104	187	12	a3	a3	NOUN
ma-104	187	13	)	)	PUNCT
ma-104	187	14	and	and	CCONJ
ma-104	187	15	condition	condition	NOUN
ma-104	187	16	(	(	PUNCT
ma-104	187	17	?	?	PUNCT
ma-104	187	18	?	?	PUNCT
ma-104	187	19	)	)	PUNCT
ma-104	188	1	‖f	‖f	DET
ma-104	188	2	′(x0)−1f	′(x0)−1f	NOUN
ma-104	188	3	(	(	PUNCT
ma-104	188	4	xi+1)‖	xi+1)‖	PROPN
ma-104	188	5	≤	≤	PROPN
ma-104	188	6	l̄	l̄	PROPN
ma-104	188	7	∫	∫	PROPN
ma-104	188	8	1	1	NUM
ma-104	188	9	0	0	NUM
ma-104	188	10	(	(	PUNCT
ma-104	188	11	‖xi+1	‖xi+1	ADP
ma-104	188	12	−	−	PROPN
ma-104	188	13	xi‖)q	xi‖)q	PROPN
ma-104	188	14	(	(	PUNCT
ma-104	188	15	3.6	3.6	NUM
ma-104	188	16	)	)	PUNCT
ma-104	188	17	≤	≤	NOUN
ma-104	188	18	l̄	l̄	VERB
ma-104	188	19	1	1	NUM
ma-104	188	20	+	+	CCONJ
ma-104	188	21	q	q	X
ma-104	188	22	(	(	PUNCT
ma-104	188	23	si+1	si+1	NOUN
ma-104	188	24	−	−	PROPN
ma-104	188	25	si)1+q	si)1+q	NOUN
ma-104	188	26	,	,	PUNCT
ma-104	188	27	where	where	SCONJ
ma-104	188	28	l̄	l̄	NOUN
ma-104	188	29	=	=	PRON
ma-104	188	30	{	{	PUNCT
ma-104	188	31	k	k	NOUN
ma-104	188	32	,	,	PUNCT
ma-104	188	33	i	i	NOUN
ma-104	188	34	=	=	NOUN
ma-104	188	35	0	0	NUM
ma-104	189	1	l	l	NOUN
ma-104	189	2	,	,	PUNCT
ma-104	189	3	i	i	PRON
ma-104	189	4	=	=	NOUN
ma-104	189	5	1	1	NUM
ma-104	189	6	,	,	PUNCT
ma-104	189	7	2	2	NUM
ma-104	189	8	,	,	PUNCT
ma-104	189	9	.	.	PUNCT
ma-104	189	10	.	.	PUNCT
ma-104	189	11	.	.	PUNCT
ma-104	190	1	.it	.it	PUNCT
ma-104	190	2	follows	follow	VERB
ma-104	190	3	by	by	ADP
ma-104	190	4	ni	ni	PROPN
ma-104	190	5	,	,	PUNCT
ma-104	190	6	estimates	estimate	NOUN
ma-104	190	7	(	(	PUNCT
ma-104	190	8	3.4	3.4	NUM
ma-104	190	9	)	)	PUNCT
ma-104	190	10	,	,	PUNCT
ma-104	190	11	(	(	PUNCT
ma-104	190	12	3.6	3.6	NUM
ma-104	190	13	)	)	PUNCT
ma-104	190	14	and	and	CCONJ
ma-104	190	15	the	the	DET
ma-104	190	16	definition	definition	NOUN
ma-104	190	17	(	(	PUNCT
ma-104	190	18	2.1	2.1	NUM
ma-104	190	19	)	)	PUNCT
ma-104	190	20	of	of	ADP
ma-104	190	21	sequence	sequence	NOUN
ma-104	190	22	{	{	PUNCT
ma-104	190	23	sn	sn	NOUN
ma-104	190	24	}	}	PUNCT
ma-104	190	25	‖xi+2	‖xi+2	PUNCT
ma-104	191	1	−	−	PROPN
ma-104	191	2	xi+1‖	xi+1‖	PROPN
ma-104	191	3	≤	≤	PROPN
ma-104	191	4	‖f	‖f	PRON
ma-104	191	5	′(xi+1)−1f	′(xi+1)−1f	NOUN
ma-104	191	6	′(x0)‖‖f	′(x0)‖‖f	X
ma-104	191	7	′(x0)−1f	′(x0)−1f	NOUN
ma-104	191	8	(	(	PUNCT
ma-104	191	9	xi+1)‖	xi+1)‖	PROPN
ma-104	191	10	,	,	PUNCT
ma-104	191	11	≤	≤	NUM
ma-104	191	12	k̃(si+1	k̃(si+1	PROPN
ma-104	191	13	−	−	PROPN
ma-104	191	14	si)2	si)2	PROPN
ma-104	191	15	2(1−	2(1−	NUM
ma-104	191	16	l̃si+1	l̃si+1	NOUN
ma-104	191	17	)	)	PUNCT
ma-104	192	1	=	=	PUNCT
ma-104	192	2	si+2	si+2	PROPN
ma-104	192	3	−	−	NUM
ma-104	192	4	si+1	si+1	NOUN
ma-104	192	5	,	,	PUNCT
ma-104	192	6	where	where	SCONJ
ma-104	192	7	k̃	k̃	PROPN
ma-104	192	8	=	=	PROPN
ma-104	192	9	{	{	PUNCT
ma-104	192	10	k	k	NOUN
ma-104	192	11	,	,	PUNCT
ma-104	192	12	i	i	NOUN
ma-104	192	13	=	=	NOUN
ma-104	192	14	0	0	NUM
ma-104	192	15	l	l	NOUN
ma-104	192	16	,	,	PUNCT
ma-104	192	17	i	i	PRON
ma-104	192	18	=	=	NOUN
ma-104	192	19	1	1	NUM
ma-104	192	20	,	,	PUNCT
ma-104	192	21	2	2	NUM
ma-104	192	22	,	,	PUNCT
ma-104	192	23	.	.	PUNCT
ma-104	192	24	.	.	PUNCT
ma-104	192	25	.	.	PUNCT
ma-104	193	1	.	.	PUNCT
ma-104	194	1	and	and	CCONJ
ma-104	194	2	l̃	l̃	PROPN
ma-104	194	3	=	=	PUNCT
ma-104	194	4	{	{	PUNCT
ma-104	194	5	k0	k0	PROPN
ma-104	194	6	,	,	PUNCT
ma-104	194	7	i	i	PROPN
ma-104	194	8	=	=	SYM
ma-104	194	9	0	0	NUM
ma-104	194	10	l0	l0	PROPN
ma-104	194	11	,	,	PUNCT
ma-104	194	12	i	i	PRON
ma-104	194	13	=	=	NOUN
ma-104	194	14	1	1	NUM
ma-104	194	15	,	,	PUNCT
ma-104	194	16	2	2	NUM
ma-104	194	17	,	,	PUNCT
ma-104	194	18	.	.	PUNCT
ma-104	194	19	.	.	PUNCT
ma-104	194	20	.	.	PUNCT
ma-104	194	21	.	.	PUNCT
ma-104	195	1	moreover	moreover	ADV
ma-104	195	2	,	,	PUNCT
ma-104	195	3	if	if	SCONJ
ma-104	195	4	v	v	ADP
ma-104	195	5	∈	∈	PROPN
ma-104	195	6	u[xi+2	u[xi+2	NOUN
ma-104	195	7	,	,	PUNCT
ma-104	195	8	s	s	NOUN
ma-104	195	9	∗	∗	NOUN
ma-104	195	10	−	−	PROPN
ma-104	195	11	si+2	si+2	AUX
ma-104	195	12	]	]	PUNCT
ma-104	195	13	it	it	PRON
ma-104	195	14	follows	follow	VERB
ma-104	195	15	‖v	‖v	PROPN
ma-104	196	1	−	−	PROPN
ma-104	197	1	xi+1‖	xi+1‖	PROPN
ma-104	197	2	≤	≤	PROPN
ma-104	197	3	‖v	‖v	NOUN
ma-104	197	4	−	−	PROPN
ma-104	197	5	xi+2‖+	xi+2‖+	NOUN
ma-104	197	6	‖xi+2	‖xi+2	PUNCT
ma-104	198	1	−	−	PROPN
ma-104	198	2	xi+1‖	xi+1‖	PROPN
ma-104	198	3	≤	≤	PROPN
ma-104	198	4	s∗	s∗	PROPN
ma-104	198	5	−	−	PROPN
ma-104	198	6	si+2	si+2	X
ma-104	199	1	+	+	CCONJ
ma-104	199	2	si+2	si+2	X
ma-104	199	3	−	−	NUM
ma-104	199	4	si+1	si+1	PROPN
ma-104	199	5	=	=	SYM
ma-104	199	6	s∗	s∗	PROPN
ma-104	199	7	−	−	PROPN
ma-104	199	8	si+1	si+1	NOUN
ma-104	199	9	.	.	PUNCT
ma-104	200	1	hence	hence	ADV
ma-104	200	2	,	,	PUNCT
ma-104	200	3	point	point	VERB
ma-104	200	4	w	w	PROPN
ma-104	200	5	∈	∈	PROPN
ma-104	200	6	u[xi+1	u[xi+1	NOUN
ma-104	200	7	,	,	PUNCT
ma-104	200	8	s	s	NOUN
ma-104	200	9	∗	∗	NOUN
ma-104	200	10	−	−	NOUN
ma-104	200	11	si+1	si+1	NOUN
ma-104	200	12	]	]	PUNCT
ma-104	200	13	completing	complete	VERB
ma-104	200	14	the	the	DET
ma-104	200	15	induction	induction	NOUN
ma-104	200	16	for	for	ADP
ma-104	200	17	items	item	NOUN
ma-104	200	18	(	(	PUNCT
ma-104	200	19	3.2	3.2	NUM
ma-104	200	20	)	)	PUNCT
ma-104	200	21	and	and	CCONJ
ma-104	200	22	(	(	PUNCT
ma-104	200	23	3.3	3.3	NUM
ma-104	200	24	)	)	PUNCT
ma-104	200	25	.	.	PUNCT
ma-104	201	1	noticethat	noticethat	DET
ma-104	201	2	scalar	scalar	ADJ
ma-104	201	3	majorizing	majorize	VERB
ma-104	201	4	sequence	sequence	NOUN
ma-104	201	5	{	{	PUNCT
ma-104	201	6	si	si	NOUN
ma-104	201	7	}	}	PUNCT
ma-104	201	8	is	be	AUX
ma-104	201	9	fundamental	fundamental	ADJ
ma-104	201	10	as	as	ADP
ma-104	201	11	convergent	convergent	NOUN
ma-104	201	12	.	.	PUNCT
ma-104	202	1	hence	hence	ADV
ma-104	202	2	,	,	PUNCT
ma-104	202	3	the	the	DET
ma-104	202	4	sequence	sequence	NOUN
ma-104	202	5	{	{	PUNCT
ma-104	202	6	xi	xi	NOUN
ma-104	202	7	}	}	PUNCT
ma-104	202	8	isalso	isalso	ADV
ma-104	202	9	convergent	convergent	NOUN
ma-104	202	10	to	to	ADP
ma-104	202	11	some	some	DET
ma-104	202	12	x∗	x∗	PROPN
ma-104	202	13	∈	∈	PROPN
ma-104	202	14	u[x0	u[x0	NOUN
ma-104	202	15	,	,	PUNCT
ma-104	202	16	s	s	PART
ma-104	202	17	∗	∗	NOUN
ma-104	202	18	]	]	PUNCT
ma-104	202	19	.	.	PUNCT
ma-104	203	1	furthermore	furthermore	ADV
ma-104	203	2	,	,	PUNCT
ma-104	203	3	let	let	VERB
ma-104	203	4	i	i	PRON
ma-104	203	5	−→	−→	VERB
ma-104	203	6	∞	∞	NUM
ma-104	203	7	in	in	ADP
ma-104	203	8	estimate	estimate	NOUN
ma-104	203	9	(	(	PUNCT
ma-104	203	10	3.6	3.6	NUM
ma-104	203	11	)	)	PUNCT
ma-104	203	12	,	,	PUNCT
ma-104	203	13	to	to	PART
ma-104	203	14	conclude	conclude	VERB
ma-104	203	15	f	f	PROPN
ma-104	203	16	(	(	PUNCT
ma-104	203	17	x∗	x∗	PROPN
ma-104	203	18	)	)	PUNCT
ma-104	203	19	=	=	SYM
ma-104	204	1	0	0	X
ma-104	204	2	.	.	X
ma-104	204	3	�	�	PROPN
ma-104	204	4	next	next	ADV
ma-104	204	5	,	,	PUNCT
ma-104	204	6	the	the	DET
ma-104	204	7	uniqueness	uniqueness	NOUN
ma-104	204	8	ball	ball	NOUN
ma-104	204	9	for	for	ADP
ma-104	204	10	a	a	DET
ma-104	204	11	solution	solution	NOUN
ma-104	204	12	is	be	AUX
ma-104	204	13	presented	present	VERB
ma-104	204	14	.	.	PUNCT
ma-104	205	1	notice	notice	VERB
ma-104	205	2	that	that	SCONJ
ma-104	205	3	not	not	PART
ma-104	205	4	all	all	DET
ma-104	205	5	condition	condition	VERB
ma-104	205	6	a	a	PRON
ma-104	205	7	are	be	AUX
ma-104	205	8	used	use	VERB
ma-104	205	9	.	.	PUNCT
ma-104	206	1	proposition	proposition	NOUN
ma-104	206	2	3.2	3.2	NUM
ma-104	206	3	.	.	PUNCT
ma-104	207	1	under	under	ADP
ma-104	207	2	center	center	ADJ
ma-104	207	3	-	-	PUNCT
ma-104	207	4	lipschitz	lipschitz	NOUN
ma-104	207	5	condition	condition	NOUN
ma-104	207	6	(	(	PUNCT
ma-104	207	7	a2	a2	PROPN
ma-104	207	8	)	)	PUNCT
ma-104	207	9	further	far	ADV
ma-104	207	10	suppose	suppose	VERB
ma-104	207	11	the	the	DET
ma-104	207	12	existence	existence	NOUN
ma-104	207	13	of	of	ADP
ma-104	207	14	a	a	DET
ma-104	207	15	solution	solution	NOUN
ma-104	207	16	p	p	X
ma-104	207	17	∈	∈	PROPN
ma-104	207	18	u(x0	u(x0	NOUN
ma-104	207	19	,	,	PUNCT
ma-104	207	20	r	r	NOUN
ma-104	207	21	)	)	PUNCT
ma-104	207	22	⊂	⊂	PROPN
ma-104	207	23	ω	ω	PROPN
ma-104	207	24	of	of	ADP
ma-104	207	25	equation	equation	NOUN
ma-104	207	26	(	(	PUNCT
ma-104	207	27	1.1	1.1	NUM
ma-104	207	28	)	)	PUNCT
ma-104	207	29	such	such	ADJ
ma-104	207	30	that	that	DET
ma-104	207	31	operator	operator	NOUN
ma-104	207	32	f	f	PROPN
ma-104	207	33	′(p	′(p	PROPN
ma-104	207	34	)	)	PUNCT
ma-104	207	35	is	be	AUX
ma-104	207	36	invertible	invertible	ADJ
ma-104	207	37	for	for	ADP
ma-104	207	38	some	some	DET
ma-104	207	39	r	r	NOUN
ma-104	207	40	>	>	X
ma-104	207	41	0	0	NUM
ma-104	207	42	;	;	PUNCT
ma-104	207	43	a	a	DET
ma-104	207	44	parameter	parameter	NOUN
ma-104	207	45	r1	r1	NOUN
ma-104	207	46	≥	≥	PRON
ma-104	207	47	r	r	NOUN
ma-104	207	48	given	give	VERB
ma-104	207	49	by	by	ADP
ma-104	207	50	r1	r1	PROPN
ma-104	207	51	=	=	SYM
ma-104	207	52	(	(	PUNCT
ma-104	207	53	1	1	NUM
ma-104	207	54	+	+	CCONJ
ma-104	207	55	q	q	PROPN
ma-104	207	56	l0	l0	NOUN
ma-104	207	57	−	−	PROPN
ma-104	207	58	rq	rq	X
ma-104	207	59	)	)	PUNCT
ma-104	207	60	1	1	NUM
ma-104	207	61	q	q	NOUN
ma-104	207	62	.	.	PUNCT
ma-104	208	1	(	(	PUNCT
ma-104	208	2	3.7	3.7	NUM
ma-104	208	3	)	)	PUNCT
ma-104	208	4	then	then	ADV
ma-104	208	5	,	,	PUNCT
ma-104	208	6	the	the	DET
ma-104	208	7	poiny	poiny	ADJ
ma-104	208	8	p	p	NOUN
ma-104	208	9	solves	solve	NOUN
ma-104	208	10	uniquely	uniquely	ADV
ma-104	208	11	equation	equation	NOUN
ma-104	208	12	f	f	X
ma-104	208	13	(	(	PUNCT
ma-104	208	14	x	x	X
ma-104	208	15	)	)	PUNCT
ma-104	208	16	=	=	SYM
ma-104	208	17	0	0	NUM
ma-104	208	18	in	in	ADP
ma-104	208	19	the	the	DET
ma-104	208	20	domain	domain	NOUN
ma-104	208	21	b2	b2	NOUN
ma-104	208	22	=	=	SYM
ma-104	208	23	u(x0	u(x0	NOUN
ma-104	208	24	,	,	PUNCT
ma-104	208	25	r1	r1	PROPN
ma-104	208	26	)	)	PUNCT
ma-104	208	27	∩ω	∩ω	PROPN
ma-104	208	28	.	.	PUNCT
ma-104	209	1	https://doi.org/10.28924/ada/ma.3.5	https://doi.org/10.28924/ada/ma.3.5	PROPN
ma-104	209	2	eur	eur	PROPN
ma-104	209	3	.	.	PUNCT
ma-104	210	1	j.	j.	PROPN
ma-104	210	2	math	math	PROPN
ma-104	210	3	.	.	PUNCT
ma-104	211	1	anal	anal	PROPN
ma-104	211	2	.	.	PUNCT
ma-104	212	1	10.28924	10.28924	NUM
ma-104	212	2	/	/	SYM
ma-104	212	3	ada	ada	PROPN
ma-104	212	4	/	/	SYM
ma-104	212	5	ma.3.5	ma.3.5	NOUN
ma-104	212	6	8	8	NUM
ma-104	212	7	proof	proof	NOUN
ma-104	212	8	.	.	PUNCT
ma-104	213	1	define	define	VERB
ma-104	213	2	linear	linear	ADJ
ma-104	213	3	operator	operator	NOUN
ma-104	213	4	q	q	PROPN
ma-104	214	1	=	=	PUNCT
ma-104	214	2	∫	∫	PROPN
ma-104	214	3	1	1	NUM
ma-104	214	4	0	0	NUM
ma-104	214	5	f	f	PROPN
ma-104	215	1	′(p̄	′(p̄	PROPN
ma-104	216	1	+	+	CCONJ
ma-104	216	2	ξ(p	ξ(p	NOUN
ma-104	216	3	−	−	NOUN
ma-104	216	4	p̄))dξ	p̄))dξ	NOUN
ma-104	216	5	for	for	ADP
ma-104	216	6	some	some	DET
ma-104	216	7	point	point	NOUN
ma-104	216	8	p̄	p̄	PROPN
ma-104	216	9	∈	∈	PROPN
ma-104	216	10	b2	b2	NOUN
ma-104	216	11	satisfying	satisfy	VERB
ma-104	216	12	f	f	PROPN
ma-104	216	13	(	(	PUNCT
ma-104	216	14	p̄	p̄	NOUN
ma-104	216	15	)	)	PUNCT
ma-104	216	16	=	=	SYM
ma-104	217	1	0	0	X
ma-104	217	2	.	.	PUNCT
ma-104	217	3	by	by	ADP
ma-104	217	4	using	use	VERB
ma-104	217	5	the	the	DET
ma-104	217	6	definition	definition	NOUN
ma-104	217	7	of	of	ADP
ma-104	217	8	r1	r1	PROPN
ma-104	217	9	,	,	PUNCT
ma-104	217	10	set	set	NOUN
ma-104	217	11	b2	b2	NOUN
ma-104	217	12	and	and	CCONJ
ma-104	217	13	condition	condition	NOUN
ma-104	217	14	(	(	PUNCT
ma-104	217	15	a2	a2	PROPN
ma-104	217	16	)	)	PUNCT
ma-104	217	17	‖f	‖f	PUNCT
ma-104	217	18	′(x0)−1(f	′(x0)−1(f	PROPN
ma-104	217	19	′(x0)−q)‖	′(x0)−q)‖	PROPN
ma-104	217	20	≤	≤	NUM
ma-104	217	21	∫	∫	PROPN
ma-104	217	22	1	1	NUM
ma-104	217	23	0	0	NUM
ma-104	217	24	l0((1−	l0((1−	PROPN
ma-104	217	25	ξ)‖x0	ξ)‖x0	NOUN
ma-104	217	26	−	−	PROPN
ma-104	217	27	p‖q	p‖q	NOUN
ma-104	217	28	+	+	CCONJ
ma-104	217	29	ξ‖x0	ξ‖x0	PROPN
ma-104	217	30	−	−	PROPN
ma-104	217	31	p̄‖q)dξ	p̄‖q)dξ	NOUN
ma-104	217	32	,	,	PUNCT
ma-104	217	33	<	<	X
ma-104	217	34	l0	l0	NOUN
ma-104	217	35	1	1	NUM
ma-104	217	36	+	+	CCONJ
ma-104	217	37	q	q	X
ma-104	217	38	(	(	PUNCT
ma-104	217	39	rq1	rq1	NOUN
ma-104	217	40	+	+	CCONJ
ma-104	217	41	rq	rq	X
ma-104	217	42	)	)	PUNCT
ma-104	217	43	=	=	SYM
ma-104	217	44	1	1	NUM
ma-104	217	45	,	,	PUNCT
ma-104	217	46	concluding	conclude	VERB
ma-104	217	47	that	that	PRON
ma-104	217	48	p	p	NOUN
ma-104	217	49	=	=	SYM
ma-104	217	50	p̄	p̄	NOUN
ma-104	217	51	,	,	PUNCT
ma-104	217	52	where	where	SCONJ
ma-104	217	53	the	the	DET
ma-104	217	54	invertability	invertability	NOUN
ma-104	217	55	of	of	ADP
ma-104	217	56	linear	linear	ADJ
ma-104	217	57	operator	operator	NOUN
ma-104	217	58	is	be	AUX
ma-104	217	59	also	also	ADV
ma-104	217	60	used	use	VERB
ma-104	217	61	together	together	ADV
ma-104	217	62	with	with	ADP
ma-104	217	63	theapproximation	theapproximation	NOUN
ma-104	217	64	0	0	PUNCT
ma-104	217	65	=	=	SYM
ma-104	217	66	f	f	X
ma-104	217	67	(	(	PUNCT
ma-104	217	68	p)−	p)−	NOUN
ma-104	217	69	f	f	X
ma-104	217	70	(	(	PUNCT
ma-104	217	71	p̄	p̄	NOUN
ma-104	217	72	)	)	PUNCT
ma-104	218	1	=	=	SYM
ma-104	218	2	q(p	q(p	PROPN
ma-104	218	3	−	−	NUM
ma-104	218	4	p̄	p̄	NOUN
ma-104	218	5	)	)	PUNCT
ma-104	218	6	.	.	PUNCT
ma-104	219	1	�	�	PROPN
ma-104	219	2	remark	remark	VERB
ma-104	219	3	3.3	3.3	NUM
ma-104	219	4	.	.	PUNCT
ma-104	220	1	(	(	PUNCT
ma-104	220	2	1	1	X
ma-104	220	3	)	)	PUNCT
ma-104	220	4	if	if	SCONJ
ma-104	220	5	conditions	condition	NOUN
ma-104	220	6	a	a	DET
ma-104	220	7	hold	hold	NOUN
ma-104	220	8	,	,	PUNCT
ma-104	220	9	set	set	VERB
ma-104	220	10	p	p	NOUN
ma-104	220	11	=	=	PUNCT
ma-104	220	12	x∗	x∗	PROPN
ma-104	220	13	and	and	CCONJ
ma-104	220	14	r	r	NOUN
ma-104	220	15	=	=	SYM
ma-104	220	16	s∗	s∗	PROPN
ma-104	220	17	in	in	ADP
ma-104	220	18	proposition	proposition	NOUN
ma-104	220	19	3.2	3.2	NUM
ma-104	220	20	.	.	PUNCT
ma-104	221	1	(	(	PUNCT
ma-104	221	2	2	2	X
ma-104	221	3	)	)	PUNCT
ma-104	221	4	lipschitz	lipschitz	NOUN
ma-104	221	5	condition	condition	NOUN
ma-104	221	6	(	(	PUNCT
ma-104	221	7	a3	a3	NOUN
ma-104	221	8	)	)	PUNCT
ma-104	221	9	can	can	AUX
ma-104	221	10	be	be	AUX
ma-104	221	11	replaced	replace	VERB
ma-104	221	12	by	by	ADP
ma-104	221	13	‖f	‖f	PRON
ma-104	221	14	′(x0)−1(f	′(x0)−1(f	PROPN
ma-104	221	15	′(z1	′(z1	NOUN
ma-104	222	1	+	+	CCONJ
ma-104	222	2	τ(z2	τ(z2	NOUN
ma-104	222	3	−	−	ADP
ma-104	223	1	z1))−	z1))−	NOUN
ma-104	223	2	f	f	NOUN
ma-104	223	3	′(z1))‖	′(z1))‖	NUM
ma-104	223	4	≤	≤	NUM
ma-104	223	5	d‖τ(z1	d‖τ(z1	PROPN
ma-104	223	6	−	−	PROPN
ma-104	223	7	z2)‖q	z2)‖q	PROPN
ma-104	223	8	(	(	PUNCT
ma-104	223	9	3.8	3.8	NUM
ma-104	223	10	)	)	PUNCT
ma-104	223	11	for	for	ADP
ma-104	223	12	all	all	DET
ma-104	223	13	z1	z1	PROPN
ma-104	223	14	∈	∈	PROPN
ma-104	223	15	b1	b1	NOUN
ma-104	223	16	and	and	CCONJ
ma-104	223	17	z2	z2	NOUN
ma-104	223	18	=	=	SYM
ma-104	223	19	z1	z1	PROPN
ma-104	223	20	−	−	PROPN
ma-104	223	21	f	f	PROPN
ma-104	223	22	′(z1)−1f	′(z1)−1f	X
ma-104	223	23	(	(	PUNCT
ma-104	223	24	z1	z1	PROPN
ma-104	223	25	)	)	PUNCT
ma-104	223	26	∈	∈	PROPN
ma-104	223	27	b1	b1	NOUN
ma-104	223	28	.	.	PUNCT
ma-104	224	1	this	this	DET
ma-104	224	2	even	even	ADV
ma-104	224	3	smaller	small	ADJ
ma-104	224	4	parameter	parameter	NOUN
ma-104	224	5	d	d	NOUN
ma-104	224	6	can	can	AUX
ma-104	224	7	replace	replace	VERB
ma-104	224	8	l	l	NOUN
ma-104	224	9	in	in	ADP
ma-104	224	10	the	the	DET
ma-104	224	11	previous	previous	ADJ
ma-104	224	12	results	result	NOUN
ma-104	224	13	.	.	PUNCT
ma-104	225	1	the	the	DET
ma-104	225	2	existence	existence	NOUN
ma-104	225	3	of	of	ADP
ma-104	225	4	iterate	iterate	NOUN
ma-104	225	5	z2	z2	PROPN
ma-104	225	6	is	be	AUX
ma-104	225	7	assured	assure	VERB
ma-104	225	8	by	by	ADP
ma-104	225	9	(	(	PUNCT
ma-104	225	10	a2	a2	PROPN
ma-104	225	11	)	)	PUNCT
ma-104	225	12	.	.	PUNCT
ma-104	226	1	4	4	X
ma-104	226	2	.	.	X
ma-104	226	3	numerical	numerical	ADJ
ma-104	226	4	experimentation	experimentation	NOUN
ma-104	226	5	three	three	NUM
ma-104	226	6	experimenta	experimenta	NOUN
ma-104	226	7	are	be	AUX
ma-104	226	8	considered	consider	VERB
ma-104	226	9	in	in	ADP
ma-104	226	10	this	this	DET
ma-104	226	11	section	section	NOUN
ma-104	226	12	.	.	PUNCT
ma-104	227	1	example	example	NOUN
ma-104	227	2	4.1	4.1	NUM
ma-104	227	3	.	.	PUNCT
ma-104	228	1	the	the	DET
ma-104	228	2	parameters	parameter	NOUN
ma-104	228	3	using	use	VERB
ma-104	228	4	example	example	NOUN
ma-104	228	5	of	of	ADP
ma-104	228	6	the	the	DET
ma-104	228	7	introduction	introduction	NOUN
ma-104	228	8	are	be	AUX
ma-104	228	9	k0	k0	PROPN
ma-104	228	10	=	=	PROPN
ma-104	228	11	µ+5	µ+5	X
ma-104	228	12	3	3	NUM
ma-104	228	13	,	,	PUNCT
ma-104	228	14	k	k	PROPN
ma-104	228	15	=	=	SYM
ma-104	228	16	l0	l0	PROPN
ma-104	228	17	=	=	PUNCT
ma-104	228	18	µ+11	µ+11	PROPN
ma-104	228	19	6	6	NUM
ma-104	228	20	.	.	PUNCT
ma-104	229	1	moreover	moreover	ADV
ma-104	229	2	,	,	PUNCT
ma-104	229	3	ω0	ω0	PROPN
ma-104	229	4	=	=	SYM
ma-104	229	5	u(1	u(1	PROPN
ma-104	229	6	,	,	PUNCT
ma-104	229	7	1	1	NUM
ma-104	229	8	−	−	PROPN
ma-104	229	9	µ	µ	NUM
ma-104	229	10	)	)	PUNCT
ma-104	229	11	∩	∩	PROPN
ma-104	229	12	u(1	u(1	PROPN
ma-104	229	13	,	,	PUNCT
ma-104	229	14	1l0	1l0	NUM
ma-104	229	15	)	)	PUNCT
ma-104	230	1	=	=	SYM
ma-104	230	2	u(1	u(1	PROPN
ma-104	230	3	,	,	PUNCT
ma-104	230	4	1l0	1l0	NUM
ma-104	230	5	)	)	PUNCT
ma-104	230	6	.	.	PUNCT
ma-104	231	1	set	set	VERB
ma-104	231	2	l	l	NOUN
ma-104	231	3	=	=	SYM
ma-104	231	4	2(1	2(1	NUM
ma-104	231	5	+	+	CCONJ
ma-104	231	6	1	1	NUM
ma-104	231	7	3−µ	3−µ	NUM
ma-104	231	8	)	)	PUNCT
ma-104	231	9	l0	l0	PROPN
ma-104	231	10	<	<	X
ma-104	231	11	l1	l1	PROPN
ma-104	231	12	and	and	CCONJ
ma-104	231	13	l	l	NOUN
ma-104	231	14	<	<	X
ma-104	231	15	l1	l1	PROPN
ma-104	231	16	for	for	ADP
ma-104	231	17	all	all	DET
ma-104	231	18	µ	µ	PRON
ma-104	231	19	∈	∈	NOUN
ma-104	231	20	(	(	PUNCT
ma-104	231	21	0	0	NUM
ma-104	231	22	,	,	PUNCT
ma-104	231	23	0.5	0.5	NUM
ma-104	231	24	)	)	PUNCT
ma-104	231	25	.	.	PUNCT
ma-104	232	1	the	the	DET
ma-104	232	2	kantorovich	kantorovich	PROPN
ma-104	232	3	criterion	criterion	NOUN
ma-104	232	4	η	η	PROPN
ma-104	232	5	≤	≤	PROPN
ma-104	232	6	1	1	NUM
ma-104	232	7	l1	l1	PROPN
ma-104	232	8	is	be	AUX
ma-104	232	9	violated	violate	VERB
ma-104	232	10	,	,	PUNCT
ma-104	232	11	since	since	SCONJ
ma-104	232	12	η	η	PROPN
ma-104	232	13	>	>	X
ma-104	232	14	1	1	NUM
ma-104	232	15	l1	l1	PROPN
ma-104	232	16	∀µ	∀µ	PROPN
ma-104	232	17	∈	∈	PROPN
ma-104	232	18	(	(	PUNCT
ma-104	232	19	0	0	NUM
ma-104	232	20	,	,	PUNCT
ma-104	232	21	0.5	0.5	NUM
ma-104	232	22	)	)	PUNCT
ma-104	232	23	,	,	PUNCT
ma-104	232	24	where	where	SCONJ
ma-104	232	25	l1	l1	PROPN
ma-104	232	26	is	be	AUX
ma-104	232	27	the	the	DET
ma-104	232	28	lipschitz	lipschitz	NOUN
ma-104	232	29	constant	constant	ADJ
ma-104	232	30	on	on	ADP
ma-104	232	31	ω	ω	PROPN
ma-104	232	32	.	.	PUNCT
ma-104	233	1	interval	interval	NOUN
ma-104	233	2	can	can	AUX
ma-104	233	3	be	be	AUX
ma-104	233	4	enlarged	enlarge	VERB
ma-104	233	5	if	if	SCONJ
ma-104	233	6	condition	condition	NOUN
ma-104	233	7	of	of	ADP
ma-104	233	8	lemma	lemma	PROPN
ma-104	233	9	2.1	2.1	NUM
ma-104	233	10	is	be	AUX
ma-104	233	11	verified	verify	VERB
ma-104	233	12	.	.	PUNCT
ma-104	234	1	then	then	ADV
ma-104	234	2	,	,	PUNCT
ma-104	234	3	for	for	ADP
ma-104	234	4	µ	µ	NOUN
ma-104	234	5	=	=	SYM
ma-104	234	6	0.4	0.4	NUM
ma-104	234	7	,	,	PUNCT
ma-104	234	8	we	we	PRON
ma-104	234	9	have	have	VERB
ma-104	234	10	the	the	DET
ma-104	234	11	following	following	NOUN
ma-104	234	12	;	;	PUNCT
ma-104	235	1	1l0	1l0	NUM
ma-104	235	2	=	=	SYM
ma-104	235	3	0.3846	0.3846	NUM
ma-104	235	4	,	,	PUNCT
ma-104	235	5	table	table	NOUN
ma-104	235	6	1	1	NUM
ma-104	235	7	.	.	PUNCT
ma-104	235	8	sequence	sequence	NOUN
ma-104	235	9	(	(	PUNCT
ma-104	235	10	2.1	2.1	NUM
ma-104	235	11	)	)	PUNCT
ma-104	235	12	n	n	CCONJ
ma-104	235	13	1	1	NUM
ma-104	235	14	2	2	NUM
ma-104	235	15	3	3	NUM
ma-104	235	16	4	4	NUM
ma-104	235	17	5	5	NUM
ma-104	235	18	6	6	NUM
ma-104	235	19	7	7	NUM
ma-104	235	20	sn+1	sn+1	NUM
ma-104	235	21	0.2000	0.2000	NUM
ma-104	235	22	0.2594	0.2594	NUM
ma-104	235	23	0.2744	0.2744	NUM
ma-104	235	24	0.2755	0.2755	NUM
ma-104	235	25	0.2755	0.2755	NUM
ma-104	235	26	0.2755	0.2755	NUM
ma-104	235	27	0.2755	0.2755	NUM
ma-104	235	28	hence	hence	ADV
ma-104	235	29	conditions	condition	NOUN
ma-104	235	30	of	of	ADP
ma-104	235	31	lemma	lemma	PROPN
ma-104	235	32	2.1	2.1	NUM
ma-104	235	33	hold	hold	NOUN
ma-104	235	34	.	.	PUNCT
ma-104	236	1	hence	hence	ADV
ma-104	236	2	condition	condition	NOUN
ma-104	236	3	(	(	PUNCT
ma-104	236	4	2.2	2.2	NUM
ma-104	236	5	)	)	PUNCT
ma-104	236	6	holds	hold	NOUN
ma-104	236	7	,	,	PUNCT
ma-104	236	8	and	and	CCONJ
ma-104	236	9	the	the	DET
ma-104	236	10	interval	interval	NOUN
ma-104	236	11	is	be	AUX
ma-104	236	12	extended	extend	VERB
ma-104	236	13	form	form	NOUN
ma-104	236	14	∅	∅	NOUN
ma-104	236	15	to	to	ADP
ma-104	236	16	[	[	X
ma-104	236	17	0.4	0.4	NUM
ma-104	236	18	,	,	PUNCT
ma-104	236	19	o.5	o.5	X
ma-104	236	20	]	]	PUNCT
ma-104	236	21	.	.	PUNCT
ma-104	237	1	example	example	NOUN
ma-104	237	2	4.2	4.2	NUM
ma-104	237	3	.	.	PUNCT
ma-104	238	1	let	let	VERB
ma-104	238	2	us	we	PRON
ma-104	238	3	consider	consider	VERB
ma-104	238	4	the	the	DET
ma-104	238	5	two	two	NUM
ma-104	238	6	point	point	NOUN
ma-104	238	7	pbvp(tpbvp	pbvp(tpbvp	NOUN
ma-104	238	8	)	)	PUNCT
ma-104	239	1	u′′	u′′	PROPN
ma-104	239	2	+	+	CCONJ
ma-104	239	3	u	u	NOUN
ma-104	239	4	3	3	NUM
ma-104	239	5	2	2	NUM
ma-104	239	6	=	=	SYM
ma-104	239	7	0	0	NUM
ma-104	239	8	u(0	u(0	NOUN
ma-104	239	9	)	)	PUNCT
ma-104	239	10	=	=	SYM
ma-104	239	11	u(1	u(1	PROPN
ma-104	239	12	)	)	PUNCT
ma-104	239	13	=	=	SYM
ma-104	240	1	0	0	X
ma-104	240	2	.	.	PUNCT
ma-104	241	1	https://doi.org/10.28924/ada/ma.3.5	https://doi.org/10.28924/ada/ma.3.5	PROPN
ma-104	241	2	eur	eur	PROPN
ma-104	241	3	.	.	PUNCT
ma-104	242	1	j.	j.	PROPN
ma-104	242	2	math	math	PROPN
ma-104	242	3	.	.	PUNCT
ma-104	243	1	anal	anal	PROPN
ma-104	243	2	.	.	PUNCT
ma-104	244	1	10.28924	10.28924	NUM
ma-104	244	2	/	/	SYM
ma-104	244	3	ada	ada	PROPN
ma-104	244	4	/	/	SYM
ma-104	244	5	ma.3.5	ma.3.5	PROPN
ma-104	244	6	9	9	NUM
ma-104	244	7	the	the	DET
ma-104	244	8	interval	interval	NOUN
ma-104	244	9	[	[	X
ma-104	244	10	0	0	NUM
ma-104	244	11	,	,	PUNCT
ma-104	244	12	1	1	NUM
ma-104	244	13	]	]	PUNCT
ma-104	244	14	is	be	AUX
ma-104	244	15	divided	divide	VERB
ma-104	244	16	into	into	ADP
ma-104	244	17	j	j	PROPN
ma-104	244	18	subintervals	subinterval	NOUN
ma-104	244	19	.	.	PUNCT
ma-104	245	1	set	set	VERB
ma-104	245	2	m	m	PROPN
ma-104	245	3	=	=	SYM
ma-104	245	4	1	1	NUM
ma-104	245	5	j	j	PROPN
ma-104	245	6	.	.	PUNCT
ma-104	246	1	denote	denote	VERB
ma-104	246	2	by	by	ADP
ma-104	246	3	w0	w0	PROPN
ma-104	246	4	=	=	SYM
ma-104	246	5	0	0	PUNCT
ma-104	246	6	<	<	X
ma-104	246	7	w1	w1	NOUN
ma-104	246	8	<	<	X
ma-104	246	9	.	.	PUNCT
ma-104	246	10	.	.	PUNCT
ma-104	246	11	.	.	PUNCT
ma-104	247	1	<	<	X
ma-104	247	2	wj	wj	X
ma-104	248	1	=	=	PUNCT
ma-104	248	2	1	1	NUM
ma-104	248	3	the	the	DET
ma-104	248	4	points	point	NOUN
ma-104	248	5	of	of	ADP
ma-104	248	6	subdivision	subdivision	NOUN
ma-104	248	7	with	with	ADP
ma-104	248	8	corresponding	correspond	VERB
ma-104	248	9	values	value	NOUN
ma-104	248	10	of	of	ADP
ma-104	248	11	the	the	DET
ma-104	248	12	function	function	NOUN
ma-104	248	13	u0	u0	NOUN
ma-104	248	14	=	=	NOUN
ma-104	248	15	u(w0	u(w0	NOUN
ma-104	248	16	)	)	PUNCT
ma-104	248	17	,	,	PUNCT
ma-104	248	18	.	.	PUNCT
ma-104	248	19	.	.	PUNCT
ma-104	248	20	.	.	PUNCT
ma-104	249	1	,	,	PUNCT
ma-104	249	2	uj	uj	PROPN
ma-104	249	3	=	=	SYM
ma-104	249	4	u(wj	u(wj	NOUN
ma-104	249	5	)	)	PUNCT
ma-104	249	6	.	.	PUNCT
ma-104	250	1	then	then	ADV
ma-104	250	2	,	,	PUNCT
ma-104	250	3	the	the	DET
ma-104	250	4	discretization	discretization	NOUN
ma-104	250	5	of	of	ADP
ma-104	250	6	u′′	u′′	PROPN
ma-104	250	7	is	be	AUX
ma-104	250	8	given	give	VERB
ma-104	250	9	by	by	ADP
ma-104	250	10	u′′k	u′′k	PROPN
ma-104	250	11	≈	≈	PROPN
ma-104	250	12	uk−1	uk−1	PROPN
ma-104	250	13	−	−	PROPN
ma-104	250	14	2uk	2uk	NOUN
ma-104	250	15	+	+	CCONJ
ma-104	250	16	uk+1	uk+1	PROPN
ma-104	250	17	m2	m2	PROPN
ma-104	250	18	,	,	PUNCT
ma-104	250	19	∀k	∀k	X
ma-104	250	20	=	=	SYM
ma-104	250	21	2	2	NUM
ma-104	250	22	,	,	PUNCT
ma-104	250	23	3	3	NUM
ma-104	250	24	,	,	PUNCT
ma-104	250	25	.	.	PUNCT
ma-104	250	26	.	.	PUNCT
ma-104	250	27	.	.	PUNCT
ma-104	251	1	j	j	PROPN
ma-104	252	1	−	−	NOUN
ma-104	252	2	1	1	NUM
ma-104	252	3	.	.	PUNCT
ma-104	252	4	notice	notice	VERB
ma-104	252	5	that	that	SCONJ
ma-104	252	6	u0	u0	ADJ
ma-104	252	7	=	=	PROPN
ma-104	252	8	uj	uj	PROPN
ma-104	252	9	=	=	NOUN
ma-104	252	10	0	0	PROPN
ma-104	252	11	.	.	PUNCT
ma-104	253	1	it	it	PRON
ma-104	253	2	follows	follow	VERB
ma-104	253	3	that	that	SCONJ
ma-104	253	4	the	the	DET
ma-104	253	5	following	follow	VERB
ma-104	253	6	system	system	NOUN
ma-104	253	7	of	of	ADP
ma-104	253	8	equations	equation	NOUN
ma-104	253	9	is	be	AUX
ma-104	253	10	obtained	obtain	VERB
ma-104	253	11	m2u	m2u	PROPN
ma-104	253	12	3	3	NUM
ma-104	253	13	2	2	NUM
ma-104	253	14	1	1	NUM
ma-104	253	15	−	−	PROPN
ma-104	253	16	2u1	2u1	NUM
ma-104	253	17	+	+	CCONJ
ma-104	253	18	u2	u2	NOUN
ma-104	253	19	=	=	SYM
ma-104	253	20	0	0	NUM
ma-104	253	21	,	,	PUNCT
ma-104	253	22	uk−1	uk−1	PROPN
ma-104	253	23	+	+	PROPN
ma-104	253	24	m2u	m2u	PROPN
ma-104	253	25	3	3	NUM
ma-104	253	26	2	2	NUM
ma-104	253	27	k	k	NOUN
ma-104	253	28	−	−	NOUN
ma-104	254	1	2uk	2uk	NOUN
ma-104	255	1	+	+	CCONJ
ma-104	255	2	uk+1	uk+1	X
ma-104	255	3	=	=	SYM
ma-104	255	4	0	0	NUM
ma-104	255	5	,	,	PUNCT
ma-104	255	6	∀k	∀k	NOUN
ma-104	255	7	=	=	SYM
ma-104	255	8	2	2	NUM
ma-104	255	9	,	,	PUNCT
ma-104	255	10	3	3	NUM
ma-104	255	11	,	,	PUNCT
ma-104	255	12	.	.	PUNCT
ma-104	255	13	.	.	PUNCT
ma-104	255	14	.	.	PUNCT
ma-104	256	1	,	,	PUNCT
ma-104	256	2	j	j	PROPN
ma-104	256	3	−	−	PROPN
ma-104	256	4	1	1	NUM
ma-104	256	5	uj−2	uj−2	PROPN
ma-104	256	6	+	+	PROPN
ma-104	256	7	m2u	m2u	PROPN
ma-104	256	8	3	3	NUM
ma-104	256	9	2	2	NUM
ma-104	256	10	j−1	j−1	PROPN
ma-104	256	11	−	−	NOUN
ma-104	256	12	2uj−1	2uj−1	NOUN
ma-104	256	13	=	=	SYM
ma-104	256	14	0	0	X
ma-104	256	15	.	.	PUNCT
ma-104	257	1	this	this	DET
ma-104	257	2	system	system	NOUN
ma-104	257	3	can	can	AUX
ma-104	257	4	be	be	AUX
ma-104	257	5	converted	convert	VERB
ma-104	257	6	into	into	ADP
ma-104	257	7	an	an	DET
ma-104	257	8	operator	operator	NOUN
ma-104	257	9	equation	equation	NOUN
ma-104	257	10	as	as	SCONJ
ma-104	257	11	follows	follow	VERB
ma-104	257	12	:	:	PUNCT
ma-104	257	13	define	define	VERB
ma-104	257	14	operator	operator	NOUN
ma-104	257	15	g	g	NOUN
ma-104	257	16	:	:	PUNCT
ma-104	257	17	rj−1	rj−1	NOUN
ma-104	257	18	−→	−→	ADJ
ma-104	257	19	rj−1	rj−1	NOUN
ma-104	257	20	whose	whose	DET
ma-104	257	21	derivative	derivative	NOUN
ma-104	257	22	is	be	AUX
ma-104	257	23	given	give	VERB
ma-104	257	24	as	as	ADP
ma-104	257	25	g′(u	g′(u	PROPN
ma-104	257	26	)	)	PUNCT
ma-104	258	1	=	=	SYM
ma-104	258	2			VERB
ma-104	258	3	3	3	NUM
ma-104	258	4	2	2	NUM
ma-104	258	5	m	m	NOUN
ma-104	258	6	2u	2u	ADJ
ma-104	258	7	1	1	NUM
ma-104	258	8	2	2	NUM
ma-104	258	9	1	1	NUM
ma-104	258	10	−	−	NUM
ma-104	258	11	2	2	NUM
ma-104	258	12	1	1	NUM
ma-104	258	13	0	0	NUM
ma-104	258	14	.	.	PUNCT
ma-104	258	15	.	.	PUNCT
ma-104	259	1	.	.	PUNCT
ma-104	260	1	0	0	NUM
ma-104	260	2	1	1	NUM
ma-104	260	3	3	3	NUM
ma-104	260	4	2	2	NUM
ma-104	260	5	m	m	NOUN
ma-104	260	6	2u	2u	ADJ
ma-104	260	7	1	1	NUM
ma-104	260	8	2	2	NUM
ma-104	260	9	2	2	NUM
ma-104	260	10	−	−	NUM
ma-104	260	11	2	2	NUM
ma-104	260	12	1	1	NUM
ma-104	260	13	0	0	NUM
ma-104	260	14	.	.	PUNCT
ma-104	260	15	.	.	PUNCT
ma-104	261	1	.	.	PUNCT
ma-104	261	2	0	0	PUNCT
ma-104	261	3	.	.	PUNCT
ma-104	261	4	.	.	PUNCT
ma-104	262	1	.	.	PUNCT
ma-104	262	2	.	.	PUNCT
ma-104	263	1	.	.	PUNCT
ma-104	263	2	.	.	PUNCT
ma-104	264	1	.	.	PUNCT
ma-104	264	2	.	.	PUNCT
ma-104	265	1	.	.	PUNCT
ma-104	265	2	.	.	PUNCT
ma-104	266	1	.	.	PUNCT
ma-104	266	2	.	.	PUNCT
ma-104	267	1	...	...	PUNCT
ma-104	267	2	...	...	PUNCT
ma-104	268	1	...	...	PUNCT
ma-104	268	2	...	...	PUNCT
ma-104	269	1	...	...	PUNCT
ma-104	269	2	0	0	NUM
ma-104	269	3	·	·	PUNCT
ma-104	269	4	·	·	PUNCT
ma-104	269	5	·	·	PUNCT
ma-104	270	1	1	1	NUM
ma-104	270	2	0	0	NUM
ma-104	270	3	3	3	NUM
ma-104	270	4	2	2	NUM
ma-104	270	5	m	m	NOUN
ma-104	270	6	2u	2u	ADJ
ma-104	270	7	1	1	NUM
ma-104	270	8	2	2	NUM
ma-104	270	9	j−1	j−1	NOUN
ma-104	270	10	−	−	NOUN
ma-104	270	11	2	2	NUM
ma-104	270	12			NOUN
ma-104	270	13	.	.	PUNCT
ma-104	271	1	let	let	VERB
ma-104	271	2	z	z	NOUN
ma-104	271	3	∈	∈	PROPN
ma-104	271	4	rj−1	rj−1	NOUN
ma-104	271	5	be	be	VERB
ma-104	271	6	arbitrary	arbitrary	ADJ
ma-104	271	7	.	.	PUNCT
ma-104	272	1	the	the	DET
ma-104	272	2	norm	norm	NOUN
ma-104	272	3	is	be	AUX
ma-104	272	4	‖z‖	‖z‖	PROPN
ma-104	272	5	=	=	PROPN
ma-104	272	6	max1≤k≤j−1	max1≤k≤j−1	PROPN
ma-104	272	7	‖zk‖	‖zk‖	PROPN
ma-104	272	8	,	,	PUNCT
ma-104	272	9	where	where	SCONJ
ma-104	272	10	as	as	SCONJ
ma-104	272	11	the	the	DET
ma-104	272	12	norm	norm	NOUN
ma-104	272	13	for	for	ADP
ma-104	272	14	g	g	PROPN
ma-104	272	15	∈	∈	PROPN
ma-104	272	16	rj−1	rj−1	NOUN
ma-104	272	17	×	×	NOUN
ma-104	272	18	rj−1	rj−1	NOUN
ma-104	272	19	is	be	AUX
ma-104	272	20	given	give	VERB
ma-104	272	21	as	as	ADP
ma-104	272	22	‖g‖	‖g‖	NUM
ma-104	272	23	=	=	SYM
ma-104	272	24	max	max	PROPN
ma-104	272	25	1≤k≤j−1	1≤k≤j−1	NUM
ma-104	272	26	j−1∑	j−1∑	NOUN
ma-104	272	27	i=1	i=1	PROPN
ma-104	272	28	‖gk	‖gk	NUM
ma-104	272	29	,	,	PUNCT
ma-104	272	30	i‖.	i‖.	NOUN
ma-104	272	31	then	then	ADV
ma-104	272	32	,	,	PUNCT
ma-104	272	33	if	if	SCONJ
ma-104	272	34	u	u	NOUN
ma-104	272	35	,	,	PUNCT
ma-104	272	36	z	z	PROPN
ma-104	272	37	∈	∈	PROPN
ma-104	272	38	rj−1	rj−1	NOUN
ma-104	272	39	for	for	ADP
ma-104	272	40	|uk	|uk	X
ma-104	272	41	|	|	CCONJ
ma-104	272	42	>	>	X
ma-104	272	43	0	0	NUM
ma-104	272	44	,	,	PUNCT
ma-104	272	45	|zk	|zk	PUNCT
ma-104	272	46	|	|	ADV
ma-104	272	47	>	>	X
ma-104	272	48	0	0	NUM
ma-104	272	49	,	,	PUNCT
ma-104	272	50	∀k	∀k	NOUN
ma-104	272	51	=	=	SYM
ma-104	272	52	1	1	NUM
ma-104	272	53	,	,	PUNCT
ma-104	272	54	2	2	NUM
ma-104	272	55	,	,	PUNCT
ma-104	272	56	.	.	PUNCT
ma-104	272	57	.	.	PUNCT
ma-104	273	1	.	.	PUNCT
ma-104	274	1	,	,	PUNCT
ma-104	275	1	j	j	PROPN
ma-104	275	2	−	−	PROPN
ma-104	275	3	1	1	NUM
ma-104	275	4	to	to	PART
ma-104	275	5	obtain	obtain	VERB
ma-104	275	6	in	in	ADP
ma-104	275	7	turn	turn	NOUN
ma-104	275	8	‖g′(u)−	‖g′(u)−	PRON
ma-104	275	9	g′(z)‖	g′(z)‖	NOUN
ma-104	275	10	=	=	PUNCT
ma-104	275	11	‖diag	‖diag	PRON
ma-104	275	12	{	{	PUNCT
ma-104	275	13	3	3	NUM
ma-104	275	14	2	2	NUM
ma-104	275	15	(	(	PUNCT
ma-104	275	16	u	u	NOUN
ma-104	275	17	1	1	NUM
ma-104	275	18	2	2	NUM
ma-104	275	19	k	k	NOUN
ma-104	275	20	−	−	PROPN
ma-104	275	21	z	z	NOUN
ma-104	275	22	1	1	NUM
ma-104	275	23	2	2	NUM
ma-104	275	24	k	k	NOUN
ma-104	275	25	)	)	PUNCT
ma-104	275	26	}	}	PUNCT
ma-104	275	27	‖	‖	PROPN
ma-104	275	28	=	=	SYM
ma-104	275	29	3	3	NUM
ma-104	275	30	2	2	NUM
ma-104	275	31	m2	m2	PROPN
ma-104	275	32	[	[	PUNCT
ma-104	275	33	max	max	PROPN
ma-104	275	34	1≤k≤j−1	1≤k≤j−1	NUM
ma-104	275	35	|uk	|uk	NUM
ma-104	275	36	−	−	PROPN
ma-104	275	37	zk	zk	PROPN
ma-104	276	1	|	|	ADV
ma-104	276	2	]	]	PUNCT
ma-104	276	3	1	1	NUM
ma-104	276	4	2	2	NUM
ma-104	276	5	=	=	SYM
ma-104	276	6	3	3	NUM
ma-104	276	7	2	2	NUM
ma-104	276	8	m2‖u	m2‖u	NUM
ma-104	276	9	−	−	PROPN
ma-104	276	10	z‖	z‖	NOUN
ma-104	276	11	1	1	NUM
ma-104	276	12	2	2	NUM
ma-104	276	13	.	.	PUNCT
ma-104	277	1	choose	choose	VERB
ma-104	277	2	as	as	ADP
ma-104	277	3	an	an	DET
ma-104	277	4	initial	initial	ADJ
ma-104	277	5	guess	guess	NOUN
ma-104	277	6	vector	vector	NOUN
ma-104	277	7	130	130	NUM
ma-104	277	8	sinπx	sinπx	NOUN
ma-104	277	9	to	to	PART
ma-104	277	10	obtain	obtain	VERB
ma-104	277	11	after	after	ADP
ma-104	277	12	four	four	NUM
ma-104	277	13	iterations	iteration	NOUN
ma-104	277	14	u0	u0	ADJ
ma-104	277	15	=	=	PUNCT
ma-104	278	1	[	[	X
ma-104	278	2	3.35740e	3.35740e	NOUN
ma-104	278	3	+	+	NOUN
ma-104	278	4	01	01	NUM
ma-104	278	5	,	,	PUNCT
ma-104	278	6	6.5202e	6.5202e	PROPN
ma-104	278	7	+	+	NOUN
ma-104	278	8	01	01	NUM
ma-104	278	9	,	,	PUNCT
ma-104	278	10	9.15664e	9.15664e	NOUN
ma-104	278	11	+	+	NUM
ma-104	278	12	01	01	NUM
ma-104	278	13	,	,	PUNCT
ma-104	278	14	1.09168e	1.09168e	PROPN
ma-104	278	15	+	+	NUM
ma-104	278	16	02	02	NUM
ma-104	278	17	,	,	PUNCT
ma-104	278	18	1.15363e	1.15363e	NOUN
ma-104	278	19	+	+	X
ma-104	278	20	02	02	NUM
ma-104	278	21	,	,	PUNCT
ma-104	278	22	1.09168e	1.09168e	PROPN
ma-104	278	23	+	+	NUM
ma-104	278	24	02	02	NUM
ma-104	278	25	,	,	PUNCT
ma-104	278	26	9.15664e	9.15664e	NOUN
ma-104	278	27	+	+	NUM
ma-104	278	28	01	01	NUM
ma-104	278	29	,	,	PUNCT
ma-104	278	30	6.52027e	6.52027e	PROPN
ma-104	278	31	+	+	CCONJ
ma-104	278	32	01	01	NUM
ma-104	278	33	,	,	PUNCT
ma-104	278	34	3.35740e	3.35740e	PROPN
ma-104	278	35	+	+	NUM
ma-104	278	36	01]tr	01]tr	NUM
ma-104	278	37	]	]	PUNCT
ma-104	278	38	.	.	PUNCT
ma-104	279	1	then	then	ADV
ma-104	279	2	,	,	PUNCT
ma-104	279	3	the	the	DET
ma-104	279	4	parameters	parameter	NOUN
ma-104	279	5	are	be	AUX
ma-104	279	6	‖q′(u0)−1‖	‖q′(u0)−1‖	PUNCT
ma-104	279	7	≤	≤	NUM
ma-104	279	8	2.5582e	2.5582e	NUM
ma-104	280	1	+	+	CCONJ
ma-104	280	2	01	01	NUM
ma-104	280	3	,	,	PUNCT
ma-104	280	4	η	η	PROPN
ma-104	280	5	=	=	PROPN
ma-104	281	1	9.15311e	9.15311e	PROPN
ma-104	281	2	−	−	PROPN
ma-104	281	3	05	05	NUM
ma-104	281	4	,	,	PUNCT
ma-104	281	5	q	q	NOUN
ma-104	281	6	=	=	SYM
ma-104	281	7	0.5	0.5	NUM
ma-104	281	8	,	,	PUNCT
ma-104	282	1	k0	k0	PROPN
ma-104	282	2	=	=	PROPN
ma-104	282	3	l0	l0	PROPN
ma-104	282	4	=	=	SYM
ma-104	283	1	k	k	NOUN
ma-104	283	2	=	=	PUNCT
ma-104	283	3	l	l	NOUN
ma-104	283	4	=	=	SYM
ma-104	284	1	3	3	NUM
ma-104	284	2	200	200	NUM
ma-104	284	3	=	=	SYM
ma-104	284	4	0.015	0.015	NUM
ma-104	284	5	.	.	PUNCT
ma-104	285	1	then	then	ADV
ma-104	285	2	,	,	PUNCT
ma-104	285	3	k0ηp	k0ηp	PROPN
ma-104	285	4	=	=	SYM
ma-104	285	5	1.4351e	1.4351e	PROPN
ma-104	285	6	−	−	NUM
ma-104	285	7	04	04	NUM
ma-104	285	8	and	and	CCONJ
ma-104	285	9	the	the	DET
ma-104	285	10	following	follow	VERB
ma-104	285	11	table	table	NOUN
ma-104	285	12	shows	show	VERB
ma-104	285	13	that	that	SCONJ
ma-104	285	14	the	the	DET
ma-104	285	15	conditions	condition	NOUN
ma-104	285	16	of	of	ADP
ma-104	285	17	lemma	lemma	PROPN
ma-104	285	18	2.1	2.1	NUM
ma-104	285	19	are	be	AUX
ma-104	285	20	satisfied	satisfied	ADJ
ma-104	285	21	.	.	PUNCT
ma-104	286	1	example	example	NOUN
ma-104	286	2	4.3	4.3	NUM
ma-104	286	3	.	.	PUNCT
ma-104	287	1	let	let	VERB
ma-104	287	2	m1	m1	PROPN
ma-104	287	3	=	=	SYM
ma-104	287	4	m2	m2	PROPN
ma-104	287	5	=	=	SYM
ma-104	287	6	c[0	c[0	PROPN
ma-104	287	7	,	,	PUNCT
ma-104	287	8	1	1	NUM
ma-104	287	9	]	]	PUNCT
ma-104	287	10	be	be	AUX
ma-104	287	11	the	the	DET
ma-104	287	12	set	set	NOUN
ma-104	287	13	of	of	ADP
ma-104	287	14	continuous	continuous	ADJ
ma-104	287	15	real	real	ADJ
ma-104	287	16	functions	function	NOUN
ma-104	287	17	on	on	ADP
ma-104	287	18	[	[	X
ma-104	287	19	0	0	NUM
ma-104	287	20	,	,	PUNCT
ma-104	287	21	1	1	NUM
ma-104	287	22	]	]	PUNCT
ma-104	287	23	.	.	PUNCT
ma-104	288	1	the	the	DET
ma-104	288	2	norm	norm	NOUN
ma-104	288	3	-	-	PUNCT
ma-104	288	4	max	max	PROPN
ma-104	288	5	is	be	AUX
ma-104	288	6	used	use	VERB
ma-104	288	7	.	.	PUNCT
ma-104	289	1	set	set	VERB
ma-104	289	2	ω	ω	PROPN
ma-104	289	3	=	=	SYM
ma-104	289	4	u[x0	u[x0	NOUN
ma-104	289	5	,	,	PUNCT
ma-104	289	6	3	3	NUM
ma-104	289	7	]	]	PUNCT
ma-104	289	8	.	.	PUNCT
ma-104	290	1	consider	consider	VERB
ma-104	290	2	hammerstein	hammerstein	PROPN
ma-104	290	3	nonlinear	nonlinear	ADJ
ma-104	290	4	integral	integral	ADJ
ma-104	290	5	operator	operator	NOUN
ma-104	290	6	h	h	NOUN
ma-104	291	1	[	[	X
ma-104	291	2	3,6	3,6	NUM
ma-104	291	3	]	]	PUNCT
ma-104	291	4	on	on	ADP
ma-104	291	5	https://doi.org/10.28924/ada/ma.3.5	https://doi.org/10.28924/ada/ma.3.5	PROPN
ma-104	291	6	eur	eur	PROPN
ma-104	291	7	.	.	PUNCT
ma-104	292	1	j.	j.	PROPN
ma-104	292	2	math	math	PROPN
ma-104	292	3	.	.	PUNCT
ma-104	293	1	anal	anal	PROPN
ma-104	293	2	.	.	PUNCT
ma-104	294	1	10.28924	10.28924	NUM
ma-104	294	2	/	/	SYM
ma-104	294	3	ada	ada	PROPN
ma-104	294	4	/	/	SYM
ma-104	294	5	ma.3.5	ma.3.5	NOUN
ma-104	294	6	10table	10table	NOUN
ma-104	295	1	2	2	NUM
ma-104	295	2	.	.	X
ma-104	295	3	sequence	sequence	NOUN
ma-104	295	4	(	(	PUNCT
ma-104	295	5	2.1	2.1	NUM
ma-104	295	6	)	)	PUNCT
ma-104	295	7	n	n	CCONJ
ma-104	295	8	1	1	NUM
ma-104	295	9	2	2	NUM
ma-104	295	10	3	3	NUM
ma-104	295	11	4	4	NUM
ma-104	295	12	5	5	NUM
ma-104	295	13	6	6	NUM
ma-104	295	14	vn+1	vn+1	NUM
ma-104	295	15	0.1435e-03	0.1435e-03	NUM
ma-104	295	16	0.1435e-03	0.1435e-03	NUM
ma-104	295	17	0.1435e-03	0.1435e-03	NUM
ma-104	295	18	0.1435e-03	0.1435e-03	NUM
ma-104	295	19	0.1435e-03	0.1435e-03	NUM
ma-104	295	20	0.1435e-03	0.1435e-03	NUM
ma-104	295	21	ω	ω	NUM
ma-104	295	22	as	as	ADP
ma-104	295	23	h(v)(z1	h(v)(z1	NOUN
ma-104	295	24	)	)	PUNCT
ma-104	295	25	=	=	VERB
ma-104	296	1	v(z1)−	v(z1)−	NOUN
ma-104	296	2	y(z1)−	y(z1)−	NOUN
ma-104	296	3	∫	∫	PROPN
ma-104	296	4	1	1	NUM
ma-104	296	5	0	0	NUM
ma-104	296	6	v(z1	v(z1	NOUN
ma-104	296	7	,	,	PUNCT
ma-104	296	8	z2)v	z2)v	ADJ
ma-104	296	9	3(z2)dz1	3(z2)dz1	NUM
ma-104	296	10	=	=	SYM
ma-104	296	11	2	2	NUM
ma-104	296	12	,	,	PUNCT
ma-104	296	13	v	v	NOUN
ma-104	296	14	∈	∈	PROPN
ma-104	296	15	c[0	c[0	NOUN
ma-104	296	16	,	,	PUNCT
ma-104	296	17	1	1	NUM
ma-104	296	18	]	]	PUNCT
ma-104	296	19	,	,	PUNCT
ma-104	296	20	z1	z1	PROPN
ma-104	296	21	∈	∈	PROPN
ma-104	297	1	[	[	X
ma-104	297	2	0	0	NUM
ma-104	297	3	,	,	PUNCT
ma-104	297	4	1	1	NUM
ma-104	297	5	]	]	PUNCT
ma-104	297	6	.	.	PUNCT
ma-104	298	1	(	(	PUNCT
ma-104	298	2	4.1	4.1	NUM
ma-104	298	3	)	)	PUNCT
ma-104	298	4	where	where	SCONJ
ma-104	298	5	function	function	VERB
ma-104	298	6	y	y	PROPN
ma-104	298	7	∈	∈	PROPN
ma-104	298	8	c[0	c[0	PROPN
ma-104	298	9	,	,	PUNCT
ma-104	298	10	1	1	NUM
ma-104	298	11	]	]	PUNCT
ma-104	298	12	,	,	PUNCT
ma-104	298	13	and	and	CCONJ
ma-104	298	14	v	v	NOUN
ma-104	298	15	is	be	AUX
ma-104	298	16	a	a	DET
ma-104	298	17	kernel	kernel	NOUN
ma-104	298	18	related	relate	VERB
ma-104	298	19	by	by	ADP
ma-104	298	20	green	green	PROPN
ma-104	298	21	’s	’s	PART
ma-104	298	22	function	function	NOUN
ma-104	298	23	v(z1	v(z1	NOUN
ma-104	298	24	,	,	PUNCT
ma-104	298	25	z2	z2	NOUN
ma-104	298	26	)	)	PUNCT
ma-104	298	27	=	=	PRON
ma-104	298	28	{	{	PUNCT
ma-104	298	29	(	(	PUNCT
ma-104	298	30	1−	1−	NUM
ma-104	298	31	z1)z2	z1)z2	NOUN
ma-104	298	32	,	,	PUNCT
ma-104	298	33	z2	z2	ADJ
ma-104	298	34	≤	≤	ADJ
ma-104	298	35	z1	z1	VERB
ma-104	298	36	z2(1−	z2(1−	NOUN
ma-104	298	37	z1	z1	PROPN
ma-104	298	38	)	)	PUNCT
ma-104	298	39	,	,	PUNCT
ma-104	298	40	z1	z1	ADJ
ma-104	298	41	≤	≤	PROPN
ma-104	298	42	z2	z2	NUM
ma-104	298	43	.	.	PUNCT
ma-104	299	1	(	(	PUNCT
ma-104	299	2	4.2	4.2	NUM
ma-104	299	3	)	)	PUNCT
ma-104	299	4	it	it	PRON
ma-104	299	5	follows	follow	VERB
ma-104	299	6	by	by	ADP
ma-104	299	7	this	this	DET
ma-104	299	8	definition	definition	NOUN
ma-104	299	9	that	that	SCONJ
ma-104	299	10	h′	h′	PROPN
ma-104	299	11	is	be	AUX
ma-104	299	12	[	[	X
ma-104	299	13	h′(v)(z)](z1	h′(v)(z)](z1	ADJ
ma-104	299	14	)	)	PUNCT
ma-104	299	15	=	=	PUNCT
ma-104	300	1	z(z1)−	z(z1)−	PROPN
ma-104	300	2	3	3	NUM
ma-104	300	3	∫	∫	NOUN
ma-104	300	4	1	1	NUM
ma-104	300	5	0	0	NUM
ma-104	300	6	v(z1	v(z1	NOUN
ma-104	300	7	,	,	PUNCT
ma-104	300	8	z2)v	z2)v	VERB
ma-104	300	9	2(z2)z(z2)dz2	2(z2)z(z2)dz2	PROPN
ma-104	300	10	(	(	PUNCT
ma-104	300	11	4.3	4.3	NUM
ma-104	300	12	)	)	PUNCT
ma-104	300	13	z	z	NOUN
ma-104	300	14	∈	∈	PROPN
ma-104	300	15	c[0	c[0	PROPN
ma-104	300	16	,	,	PUNCT
ma-104	300	17	1	1	NUM
ma-104	300	18	]	]	PUNCT
ma-104	300	19	,	,	PUNCT
ma-104	300	20	z1	z1	PROPN
ma-104	300	21	∈	∈	PROPN
ma-104	301	1	[	[	X
ma-104	301	2	0	0	NUM
ma-104	301	3	,	,	PUNCT
ma-104	301	4	1	1	NUM
ma-104	301	5	]	]	PUNCT
ma-104	301	6	.	.	PUNCT
ma-104	302	1	pick	pick	VERB
ma-104	302	2	x0(z1	x0(z1	NOUN
ma-104	302	3	)	)	PUNCT
ma-104	302	4	=	=	SYM
ma-104	302	5	y(z1	y(z1	X
ma-104	302	6	)	)	PUNCT
ma-104	302	7	=	=	SYM
ma-104	303	1	1	1	X
ma-104	303	2	.	.	PUNCT
ma-104	304	1	it	it	PRON
ma-104	304	2	then	then	ADV
ma-104	304	3	follows	follow	VERB
ma-104	304	4	from	from	ADP
ma-104	304	5	(	(	PUNCT
ma-104	304	6	4.1)-(4.3	4.1)-(4.3	NOUN
ma-104	304	7	)	)	PUNCT
ma-104	305	1	that	that	PRON
ma-104	305	2	h′(x0)−1	h′(x0)−1	PRON
ma-104	305	3	∈	∈	PROPN
ma-104	305	4	l(m2,m1	l(m2,m1	PROPN
ma-104	305	5	)	)	PUNCT
ma-104	305	6	,	,	PUNCT
ma-104	305	7	‖i	‖i	NOUN
ma-104	305	8	−h′(x0)‖	−h′(x0)‖	NOUN
ma-104	305	9	<	<	X
ma-104	305	10	0.375	0.375	NUM
ma-104	305	11	,	,	PUNCT
ma-104	305	12	‖h′(x0)−1‖	‖h′(x0)−1‖	VERB
ma-104	305	13	≤	≤	ADJ
ma-104	305	14	1.6	1.6	NUM
ma-104	305	15	,	,	PUNCT
ma-104	305	16	η	η	PROPN
ma-104	305	17	=	=	PROPN
ma-104	305	18	0.2	0.2	NUM
ma-104	305	19	,	,	PUNCT
ma-104	305	20	l0	l0	PROPN
ma-104	305	21	=	=	NOUN
ma-104	305	22	2.4	2.4	NUM
ma-104	305	23	,	,	PUNCT
ma-104	305	24	l1	l1	PROPN
ma-104	305	25	=	=	PROPN
ma-104	305	26	3.6	3.6	NUM
ma-104	305	27	,	,	PUNCT
ma-104	305	28	and	and	CCONJ
ma-104	305	29	ω0	ω0	ADV
ma-104	305	30	=	=	SYM
ma-104	305	31	u(x0	u(x0	NOUN
ma-104	305	32	,	,	PUNCT
ma-104	305	33	3	3	NUM
ma-104	305	34	)	)	PUNCT
ma-104	305	35	∩	∩	ADJ
ma-104	305	36	u(x0	u(x0	NOUN
ma-104	305	37	,	,	PUNCT
ma-104	305	38	0.4167	0.4167	NUM
ma-104	305	39	)	)	PUNCT
ma-104	305	40	=	=	SYM
ma-104	305	41	u(x0	u(x0	NOUN
ma-104	305	42	,	,	PUNCT
ma-104	305	43	0.4167	0.4167	NUM
ma-104	305	44	)	)	PUNCT
ma-104	305	45	,	,	PUNCT
ma-104	305	46	so	so	ADV
ma-104	305	47	l	l	NOUN
ma-104	305	48	=	=	SYM
ma-104	305	49	1.5	1.5	NUM
ma-104	305	50	.	.	PUNCT
ma-104	306	1	notice	notice	VERB
ma-104	306	2	that	that	SCONJ
ma-104	306	3	l0	l0	PROPN
ma-104	306	4	<	<	X
ma-104	306	5	l1	l1	PROPN
ma-104	306	6	and	and	CCONJ
ma-104	306	7	l	l	NOUN
ma-104	306	8	<	<	X
ma-104	306	9	l1	l1	PROPN
ma-104	306	10	.	.	PUNCT
ma-104	307	1	set	set	VERB
ma-104	307	2	k0	k0	PROPN
ma-104	307	3	=	=	PROPN
ma-104	307	4	k	k	PROPN
ma-104	307	5	=	=	SYM
ma-104	307	6	l0	l0	PROPN
ma-104	307	7	.	.	PUNCT
ma-104	308	1	the	the	DET
ma-104	308	2	kantorovich	kantorovich	PROPN
ma-104	308	3	convergence	convergence	NOUN
ma-104	308	4	criterion	criterion	NOUN
ma-104	308	5	(	(	PUNCT
ma-104	308	6	a3	a3	NOUN
ma-104	308	7	)	)	PUNCT
ma-104	308	8	is	be	AUX
ma-104	308	9	not	not	PART
ma-104	308	10	satisfied	satisfied	ADJ
ma-104	308	11	,	,	PUNCT
ma-104	308	12	since	since	SCONJ
ma-104	308	13	2l1η	2l1η	NUM
ma-104	308	14	=	=	SYM
ma-104	308	15	1.44	1.44	NUM
ma-104	308	16	>	>	SYM
ma-104	308	17	1	1	X
ma-104	308	18	.	.	PUNCT
ma-104	309	1	therefore	therefore	ADV
ma-104	309	2	convergence	convergence	NOUN
ma-104	309	3	of	of	ADP
ma-104	309	4	ni	ni	PROPN
ma-104	309	5	is	be	AUX
ma-104	309	6	not	not	PART
ma-104	309	7	guaranteed	guarantee	VERB
ma-104	309	8	.	.	PUNCT
ma-104	310	1	however	however	ADV
ma-104	310	2	,	,	PUNCT
ma-104	310	3	the	the	DET
ma-104	310	4	new	new	ADJ
ma-104	310	5	condition	condition	NOUN
ma-104	310	6	(	(	PUNCT
ma-104	310	7	2.7	2.7	NUM
ma-104	310	8	)	)	PUNCT
ma-104	310	9	is	be	AUX
ma-104	310	10	satisfied	satisfied	ADJ
ma-104	310	11	,	,	PUNCT
ma-104	310	12	since	since	SCONJ
ma-104	310	13	2lη	2lη	ADJ
ma-104	310	14	=	=	PUNCT
ma-104	310	15	0.6	0.6	NUM
ma-104	310	16	<	<	X
ma-104	310	17	1	1	NUM
ma-104	310	18	.	.	NOUN
ma-104	310	19	5	5	NUM
ma-104	310	20	.	.	PUNCT
ma-104	310	21	conclusions	conclusion	NOUN
ma-104	310	22	an	an	DET
ma-104	310	23	updated	update	VERB
ma-104	310	24	and	and	CCONJ
ma-104	310	25	weaker	weak	ADJ
ma-104	310	26	unified	unified	ADJ
ma-104	310	27	framework	framework	NOUN
ma-104	310	28	is	be	AUX
ma-104	310	29	presented	present	VERB
ma-104	310	30	for	for	ADP
ma-104	310	31	ni	ni	PROPN
ma-104	310	32	.	.	PUNCT
ma-104	310	33	the	the	DET
ma-104	310	34	new	new	ADJ
ma-104	310	35	analysis	analysis	NOUN
ma-104	310	36	is	be	AUX
ma-104	310	37	finer	fine	ADJ
ma-104	310	38	thanbefore	thanbefore	ADJ
ma-104	310	39	.	.	PUNCT
ma-104	311	1	convergence	convergence	NOUN
ma-104	311	2	order	order	NOUN
ma-104	311	3	1	1	NUM
ma-104	312	1	+	+	CCONJ
ma-104	312	2	q	q	NOUN
ma-104	312	3	is	be	AUX
ma-104	312	4	also	also	ADV
ma-104	312	5	recovered	recover	VERB
ma-104	312	6	by	by	ADP
ma-104	312	7	choosing	choose	VERB
ma-104	312	8	a	a	DET
ma-104	312	9	larger	large	ADJ
ma-104	312	10	upper	upper	NOUN
ma-104	312	11	bound	bind	VERB
ma-104	312	12	on	on	ADP
ma-104	312	13	t.	t.	PROPN
ma-104	312	14	newlipschitz	newlipschitz	PROPN
ma-104	312	15	or	or	CCONJ
ma-104	312	16	hölder	hölder	NOUN
ma-104	312	17	parameters	parameter	NOUN
ma-104	312	18	are	be	AUX
ma-104	312	19	smaller	small	ADJ
ma-104	312	20	and	and	CCONJ
ma-104	312	21	specilizations	specilization	NOUN
ma-104	312	22	of	of	ADP
ma-104	312	23	previous	previous	ADJ
ma-104	312	24	parameters	parameter	NOUN
ma-104	312	25	.	.	PUNCT
ma-104	313	1	the	the	DET
ma-104	313	2	newtheory	newtheory	NOUN
ma-104	313	3	can	can	AUX
ma-104	313	4	always	always	ADV
ma-104	313	5	replace	replace	VERB
ma-104	313	6	previous	previous	ADJ
ma-104	313	7	ones	one	NOUN
ma-104	313	8	due	due	ADJ
ma-104	313	9	to	to	ADP
ma-104	313	10	weaker	weak	ADJ
ma-104	313	11	criterion	criterion	NOUN
ma-104	313	12	.	.	PUNCT
ma-104	314	1	the	the	DET
ma-104	314	2	strategy	strategy	NOUN
ma-104	314	3	can	can	AUX
ma-104	314	4	be	be	AUX
ma-104	314	5	applied	apply	VERB
ma-104	314	6	onother	onother	ADJ
ma-104	314	7	iterations	iteration	NOUN
ma-104	315	1	[	[	X
ma-104	315	2	2	2	NUM
ma-104	315	3	,	,	PUNCT
ma-104	315	4	3	3	NUM
ma-104	315	5	,	,	PUNCT
ma-104	315	6	7	7	NUM
ma-104	315	7	,	,	PUNCT
ma-104	315	8	11	11	NUM
ma-104	315	9	]	]	PUNCT
ma-104	315	10	.	.	PUNCT
ma-104	316	1	references	reference	NOUN
ma-104	316	2	[	[	X
ma-104	316	3	1	1	X
ma-104	316	4	]	]	PUNCT
ma-104	316	5	j.	j.	PROPN
ma-104	316	6	appell	appell	PROPN
ma-104	316	7	,	,	PUNCT
ma-104	316	8	e.d	e.d	PROPN
ma-104	316	9	.	.	PROPN
ma-104	316	10	pascale	pascale	PROPN
ma-104	316	11	,	,	PUNCT
ma-104	316	12	j.v	j.v	PROPN
ma-104	316	13	.	.	PROPN
ma-104	317	1	lysenko	lysenko	PROPN
ma-104	317	2	,	,	PUNCT
ma-104	317	3	p.p	p.p	PROPN
ma-104	317	4	.	.	PROPN
ma-104	317	5	zabrejko	zabrejko	PROPN
ma-104	317	6	,	,	PUNCT
ma-104	317	7	new	new	ADJ
ma-104	317	8	results	result	NOUN
ma-104	317	9	on	on	ADP
ma-104	317	10	newton	newton	PROPN
ma-104	317	11	-	-	PUNCT
ma-104	317	12	kantorovich	kantorovich	PROPN
ma-104	317	13	approximations	approximation	NOUN
ma-104	317	14	with	with	ADP
ma-104	317	15	appli	appli	PROPN
ma-104	317	16	-	-	PUNCT
ma-104	317	17	cations	cation	NOUN
ma-104	317	18	to	to	PART
ma-104	317	19	nonlinear	nonlinear	VERB
ma-104	317	20	integral	integral	ADJ
ma-104	317	21	equations	equation	NOUN
ma-104	317	22	,	,	PUNCT
ma-104	317	23	numer	numer	PROPN
ma-104	317	24	.	.	PUNCT
ma-104	318	1	funct	funct	PROPN
ma-104	318	2	.	.	PUNCT
ma-104	319	1	anal	anal	PROPN
ma-104	319	2	.	.	PUNCT
ma-104	320	1	optim	optim	PROPN
ma-104	320	2	.	.	PUNCT
ma-104	321	1	18	18	NUM
ma-104	321	2	(	(	PUNCT
ma-104	321	3	1997	1997	NUM
ma-104	321	4	)	)	PUNCT
ma-104	321	5	1–17	1–17	NOUN
ma-104	321	6	.	.	PUNCT
ma-104	322	1	https://doi.org/10.1080/	https://doi.org/10.1080/	NOUN
ma-104	322	2	01630569708816744.[2	01630569708816744.[2	NUM
ma-104	322	3	]	]	X
ma-104	322	4	i.k	i.k	PROPN
ma-104	322	5	.	.	PROPN
ma-104	322	6	argyros	argyros	PROPN
ma-104	322	7	,	,	PUNCT
ma-104	322	8	unified	unified	ADJ
ma-104	322	9	convergence	convergence	NOUN
ma-104	322	10	criteria	criterion	NOUN
ma-104	322	11	for	for	ADP
ma-104	322	12	iterative	iterative	NOUN
ma-104	322	13	banach	banach	NOUN
ma-104	322	14	space	space	NOUN
ma-104	322	15	valued	value	VERB
ma-104	322	16	methods	method	NOUN
ma-104	322	17	with	with	ADP
ma-104	322	18	applications	application	NOUN
ma-104	322	19	,	,	PUNCT
ma-104	322	20	mathematics.9	mathematics.9	NOUN
ma-104	322	21	(	(	PUNCT
ma-104	322	22	2021	2021	NUM
ma-104	322	23	)	)	PUNCT
ma-104	322	24	1942	1942	NUM
ma-104	322	25	.	.	PUNCT
ma-104	323	1	https://doi.org/10.3390/math9161942.[3	https://doi.org/10.3390/math9161942.[3	PROPN
ma-104	323	2	]	]	PUNCT
ma-104	323	3	i.k	i.k	PROPN
ma-104	323	4	.	.	PROPN
ma-104	323	5	argyros	argyros	PROPN
ma-104	323	6	,	,	PUNCT
ma-104	323	7	the	the	DET
ma-104	323	8	theory	theory	NOUN
ma-104	323	9	and	and	CCONJ
ma-104	323	10	applications	application	NOUN
ma-104	323	11	of	of	ADP
ma-104	323	12	iteration	iteration	NOUN
ma-104	323	13	methods	method	NOUN
ma-104	323	14	,	,	PUNCT
ma-104	323	15	2nd	2nd	PROPN
ma-104	323	16	edition	edition	NOUN
ma-104	323	17	,	,	PUNCT
ma-104	323	18	crc	crc	NOUN
ma-104	323	19	press	press	PROPN
ma-104	323	20	,	,	PUNCT
ma-104	323	21	boca	boca	PROPN
ma-104	323	22	raton	raton	PROPN
ma-104	323	23	,	,	PUNCT
ma-104	323	24	2022	2022	NUM
ma-104	323	25	.	.	PUNCT
ma-104	324	1	https	https	NOUN
ma-104	324	2	:	:	PUNCT
ma-104	325	1	//doi.org/10.1201/9781003128915	//doi.org/10.1201/9781003128915	PROPN
ma-104	325	2	.	.	PUNCT
ma-104	326	1	https://doi.org/10.28924/ada/ma.3.5	https://doi.org/10.28924/ada/ma.3.5	PROPN
ma-104	326	2	https://doi.org/10.1080/01630569708816744	https://doi.org/10.1080/01630569708816744	NOUN
ma-104	326	3	https://doi.org/10.1080/01630569708816744	https://doi.org/10.1080/01630569708816744	X
ma-104	326	4	https://doi.org/10.3390/math9161942	https://doi.org/10.3390/math9161942	NOUN
ma-104	326	5	https://doi.org/10.1201/9781003128915	https://doi.org/10.1201/9781003128915	NOUN
ma-104	326	6	https://doi.org/10.1201/9781003128915	https://doi.org/10.1201/9781003128915	NOUN
ma-104	326	7	eur	eur	PROPN
ma-104	326	8	.	.	PUNCT
ma-104	327	1	j.	j.	PROPN
ma-104	327	2	math	math	PROPN
ma-104	327	3	.	.	PUNCT
ma-104	328	1	anal	anal	PROPN
ma-104	328	2	.	.	PUNCT
ma-104	329	1	10.28924	10.28924	NUM
ma-104	329	2	/	/	SYM
ma-104	329	3	ada	ada	PROPN
ma-104	329	4	/	/	SYM
ma-104	329	5	ma.3.5	ma.3.5	NOUN
ma-104	329	6	11	11	NUM
ma-104	329	7	[	[	X
ma-104	329	8	4	4	NUM
ma-104	329	9	]	]	X
ma-104	329	10	s.	s.	PROPN
ma-104	329	11	singh	singh	PROPN
ma-104	329	12	,	,	PUNCT
ma-104	329	13	e.	e.	PROPN
ma-104	329	14	martínez	martínez	PROPN
ma-104	329	15	,	,	PUNCT
ma-104	329	16	p.	p.	PROPN
ma-104	329	17	maroju	maroju	PROPN
ma-104	329	18	,	,	PUNCT
ma-104	329	19	r.	r.	PROPN
ma-104	329	20	behl	behl	PROPN
ma-104	329	21	,	,	PUNCT
ma-104	329	22	a	a	DET
ma-104	329	23	study	study	NOUN
ma-104	329	24	of	of	ADP
ma-104	329	25	the	the	DET
ma-104	329	26	local	local	ADJ
ma-104	329	27	convergence	convergence	NOUN
ma-104	329	28	of	of	ADP
ma-104	329	29	a	a	DET
ma-104	329	30	fifth	fifth	ADJ
ma-104	329	31	order	order	NOUN
ma-104	329	32	iterative	iterative	NOUN
ma-104	329	33	method	method	NOUN
ma-104	329	34	,	,	PUNCT
ma-104	329	35	indianj	indianj	ADJ
ma-104	329	36	.	.	PUNCT
ma-104	330	1	pure	pure	ADJ
ma-104	330	2	appl	appl	PROPN
ma-104	330	3	.	.	PUNCT
ma-104	330	4	math	math	NOUN
ma-104	330	5	.	.	PUNCT
ma-104	331	1	51	51	NUM
ma-104	331	2	(	(	PUNCT
ma-104	331	3	2020	2020	NUM
ma-104	331	4	)	)	PUNCT
ma-104	332	1	439–455	439–455	NUM
ma-104	332	2	.	.	PUNCT
ma-104	333	1	https://doi.org/10.1007/s13226-020-0409-5.[5	https://doi.org/10.1007/s13226-020-0409-5.[5	PRON
ma-104	333	2	]	]	X
ma-104	333	3	f.	f.	PROPN
ma-104	333	4	cianciaruso	cianciaruso	PROPN
ma-104	333	5	,	,	PUNCT
ma-104	333	6	e.	e.	PROPN
ma-104	333	7	de	de	PROPN
ma-104	333	8	pascale	pascale	PROPN
ma-104	333	9	,	,	PUNCT
ma-104	333	10	newton	newton	PROPN
ma-104	333	11	–	–	PUNCT
ma-104	333	12	kantorovich	kantorovich	PROPN
ma-104	333	13	approximations	approximation	NOUN
ma-104	333	14	when	when	SCONJ
ma-104	333	15	the	the	DET
ma-104	333	16	derivative	derivative	NOUN
ma-104	333	17	is	be	AUX
ma-104	333	18	hölderian	hölderian	ADJ
ma-104	333	19	:	:	PUNCT
ma-104	333	20	old	old	ADJ
ma-104	333	21	and	and	CCONJ
ma-104	333	22	newresults	newresult	NOUN
ma-104	333	23	,	,	PUNCT
ma-104	333	24	numer	numer	PROPN
ma-104	333	25	.	.	PUNCT
ma-104	334	1	funct	funct	PROPN
ma-104	334	2	.	.	PUNCT
ma-104	335	1	anal	anal	PROPN
ma-104	335	2	.	.	PUNCT
ma-104	336	1	optim	optim	PROPN
ma-104	336	2	.	.	PUNCT
ma-104	337	1	24	24	NUM
ma-104	337	2	(	(	PUNCT
ma-104	337	3	2003	2003	NUM
ma-104	337	4	)	)	PUNCT
ma-104	338	1	713–723	713–723	NUM
ma-104	338	2	.	.	PUNCT
ma-104	339	1	https://doi.org/10.1081/nfa-120026367.[6	https://doi.org/10.1081/nfa-120026367.[6	PRON
ma-104	339	2	]	]	X
ma-104	339	3	j.a	j.a	PROPN
ma-104	339	4	.	.	PROPN
ma-104	339	5	ezquerro	ezquerro	PROPN
ma-104	339	6	,	,	PUNCT
ma-104	339	7	m.a	m.a	PROPN
ma-104	339	8	.	.	PROPN
ma-104	339	9	hernandez	hernandez	PROPN
ma-104	339	10	,	,	PUNCT
ma-104	339	11	newton	newton	PROPN
ma-104	339	12	’s	’s	PART
ma-104	339	13	scheme	scheme	NOUN
ma-104	339	14	:	:	PUNCT
ma-104	339	15	an	an	DET
ma-104	339	16	updated	update	VERB
ma-104	339	17	approach	approach	NOUN
ma-104	339	18	of	of	ADP
ma-104	339	19	kantorovich	kantorovich	PROPN
ma-104	339	20	’s	’s	PART
ma-104	339	21	theory	theory	NOUN
ma-104	339	22	,	,	PUNCT
ma-104	339	23	cham	cham	PROPN
ma-104	339	24	switzerland,2018.[7	switzerland,2018.[7	NOUN
ma-104	339	25	]	]	X
ma-104	339	26	l.v	l.v	PROPN
ma-104	339	27	.	.	PROPN
ma-104	339	28	kantorovich	kantorovich	PROPN
ma-104	339	29	,	,	PUNCT
ma-104	339	30	g.p	g.p	PROPN
ma-104	339	31	.	.	PROPN
ma-104	339	32	akilov	akilov	PROPN
ma-104	339	33	,	,	PUNCT
ma-104	339	34	functional	functional	ADJ
ma-104	339	35	analysis	analysis	NOUN
ma-104	339	36	,	,	PUNCT
ma-104	339	37	pergamon	pergamon	PROPN
ma-104	339	38	press	press	PROPN
ma-104	339	39	,	,	PUNCT
ma-104	339	40	oxford	oxford	PROPN
ma-104	339	41	,	,	PUNCT
ma-104	339	42	1982.[8	1982.[8	NUM
ma-104	339	43	]	]	X
ma-104	339	44	f.a	f.a	PROPN
ma-104	339	45	.	.	PROPN
ma-104	339	46	potra	potra	PROPN
ma-104	339	47	,	,	PUNCT
ma-104	339	48	v.	v.	ADP
ma-104	339	49	pták	pták	ADJ
ma-104	339	50	,	,	PUNCT
ma-104	339	51	nondiscrete	nondiscrete	ADJ
ma-104	339	52	induction	induction	NOUN
ma-104	339	53	and	and	CCONJ
ma-104	339	54	iterative	iterative	NOUN
ma-104	339	55	processes	process	NOUN
ma-104	339	56	,	,	PUNCT
ma-104	339	57	research	research	NOUN
ma-104	339	58	notes	note	NOUN
ma-104	339	59	in	in	ADP
ma-104	339	60	mathematics	mathematic	NOUN
ma-104	339	61	,	,	PUNCT
ma-104	339	62	103	103	NUM
ma-104	339	63	.	.	PUNCT
ma-104	340	1	pitman(advanced	pitman(advance	VERB
ma-104	340	2	publishing	publishing	NOUN
ma-104	340	3	program	program	NOUN
ma-104	340	4	)	)	PUNCT
ma-104	340	5	,	,	PUNCT
ma-104	340	6	boston	boston	PROPN
ma-104	340	7	,	,	PUNCT
ma-104	340	8	1984.[9	1984.[9	NUM
ma-104	340	9	]	]	X
ma-104	340	10	p.d	p.d	PROPN
ma-104	340	11	.	.	PROPN
ma-104	340	12	proinov	proinov	PROPN
ma-104	340	13	,	,	PUNCT
ma-104	340	14	new	new	ADJ
ma-104	340	15	general	general	ADJ
ma-104	340	16	convergence	convergence	NOUN
ma-104	340	17	theory	theory	NOUN
ma-104	340	18	for	for	ADP
ma-104	340	19	iterative	iterative	NOUN
ma-104	340	20	processes	process	NOUN
ma-104	340	21	and	and	CCONJ
ma-104	340	22	its	its	PRON
ma-104	340	23	applications	application	NOUN
ma-104	340	24	to	to	ADP
ma-104	340	25	newton	newton	PROPN
ma-104	340	26	–	–	PUNCT
ma-104	340	27	kantorovichtype	kantorovichtype	NOUN
ma-104	340	28	theorems	theorems	PROPN
ma-104	340	29	,	,	PUNCT
ma-104	340	30	j.	j.	PROPN
ma-104	340	31	complex	complex	PROPN
ma-104	340	32	.	.	PUNCT
ma-104	341	1	26	26	NUM
ma-104	341	2	(	(	PUNCT
ma-104	341	3	2010	2010	NUM
ma-104	341	4	)	)	PUNCT
ma-104	342	1	3–42	3–42	PROPN
ma-104	342	2	.	.	PUNCT
ma-104	342	3	https://doi.org/10.1016/j.jco.2009.05.001.[10	https://doi.org/10.1016/j.jco.2009.05.001.[10	PROPN
ma-104	342	4	]	]	PUNCT
ma-104	342	5	r.	r.	PROPN
ma-104	342	6	verma	verma	PROPN
ma-104	342	7	,	,	PUNCT
ma-104	342	8	new	new	ADJ
ma-104	342	9	trends	trend	NOUN
ma-104	342	10	in	in	ADP
ma-104	342	11	fractional	fractional	ADJ
ma-104	342	12	programming	programming	NOUN
ma-104	342	13	,	,	PUNCT
ma-104	342	14	nova	nova	PROPN
ma-104	342	15	science	science	NOUN
ma-104	342	16	publisher	publisher	NOUN
ma-104	342	17	,	,	PUNCT
ma-104	342	18	new	new	PROPN
ma-104	342	19	york	york	PROPN
ma-104	342	20	,	,	PUNCT
ma-104	342	21	usa	usa	PROPN
ma-104	342	22	,	,	PUNCT
ma-104	342	23	2019.[11	2019.[11	NUM
ma-104	342	24	]	]	PUNCT
ma-104	342	25	t.	t.	PROPN
ma-104	342	26	yamamoto	yamamoto	PROPN
ma-104	342	27	,	,	PUNCT
ma-104	342	28	historical	historical	ADJ
ma-104	342	29	developments	development	NOUN
ma-104	342	30	in	in	ADP
ma-104	342	31	convergence	convergence	NOUN
ma-104	342	32	analysis	analysis	NOUN
ma-104	342	33	for	for	ADP
ma-104	342	34	newton	newton	PROPN
ma-104	342	35	’s	’s	PART
ma-104	342	36	and	and	CCONJ
ma-104	342	37	newton	newton	PROPN
ma-104	342	38	-	-	PUNCT
ma-104	342	39	like	like	ADJ
ma-104	342	40	methods	method	NOUN
ma-104	342	41	,	,	PUNCT
ma-104	342	42	j.	j.	PROPN
ma-104	342	43	comput.appl	comput.appl	PROPN
ma-104	342	44	.	.	PUNCT
ma-104	342	45	math	math	NOUN
ma-104	342	46	.	.	PUNCT
ma-104	343	1	124	124	NUM
ma-104	343	2	(	(	PUNCT
ma-104	343	3	2000	2000	NUM
ma-104	343	4	)	)	PUNCT
ma-104	343	5	1–23	1–23	NOUN
ma-104	343	6	.	.	PUNCT
ma-104	344	1	https://doi.org/10.1016/s0377-0427(00)00417-9.[12	https://doi.org/10.1016/s0377-0427(00)00417-9.[12	PROPN
ma-104	344	2	]	]	X
ma-104	344	3	p.p	p.p	PROPN
ma-104	344	4	.	.	PROPN
ma-104	344	5	zabrejko	zabrejko	PROPN
ma-104	344	6	,	,	PUNCT
ma-104	344	7	d.f	d.f	PROPN
ma-104	344	8	.	.	PROPN
ma-104	344	9	nguen	nguen	PROPN
ma-104	344	10	,	,	PUNCT
ma-104	344	11	the	the	DET
ma-104	344	12	majorant	majorant	NOUN
ma-104	344	13	method	method	NOUN
ma-104	344	14	in	in	ADP
ma-104	344	15	the	the	DET
ma-104	344	16	theory	theory	NOUN
ma-104	344	17	of	of	ADP
ma-104	344	18	newton	newton	PROPN
ma-104	344	19	-	-	PUNCT
ma-104	344	20	kantorovich	kantorovich	PROPN
ma-104	344	21	approximations	approximation	NOUN
ma-104	344	22	and	and	CCONJ
ma-104	344	23	the	the	DET
ma-104	344	24	ptákerror	ptákerror	NOUN
ma-104	344	25	estimates	estimate	NOUN
ma-104	344	26	,	,	PUNCT
ma-104	344	27	numer	numer	PROPN
ma-104	344	28	.	.	PUNCT
ma-104	345	1	funct	funct	PROPN
ma-104	345	2	.	.	PUNCT
ma-104	346	1	anal	anal	PROPN
ma-104	346	2	.	.	PUNCT
ma-104	347	1	optim	optim	PROPN
ma-104	347	2	.	.	PUNCT
ma-104	348	1	9	9	NUM
ma-104	348	2	(	(	PUNCT
ma-104	348	3	1987	1987	NUM
ma-104	348	4	)	)	PUNCT
ma-104	349	1	671–684	671–684	NUM
ma-104	349	2	.	.	PUNCT
ma-104	350	1	https://doi.org/10.1080/01630568708816254	https://doi.org/10.1080/01630568708816254	ADJ
ma-104	350	2	.	.	PUNCT
ma-104	351	1	https://doi.org/10.28924/ada/ma.3.5	https://doi.org/10.28924/ada/ma.3.5	PROPN
ma-104	351	2	https://doi.org/10.1007/s13226-020-0409-5	https://doi.org/10.1007/s13226-020-0409-5	NUM
ma-104	351	3	https://doi.org/10.1081/nfa-120026367	https://doi.org/10.1081/nfa-120026367	X
ma-104	351	4	https://doi.org/10.1016/j.jco.2009.05.001	https://doi.org/10.1016/j.jco.2009.05.001	PROPN
ma-104	351	5	https://doi.org/10.1016/s0377-0427(00)00417-9	https://doi.org/10.1016/s0377-0427(00)00417-9	VERB
ma-104	351	6	https://doi.org/10.1080/01630568708816254	https://doi.org/10.1080/01630568708816254	PROPN
ma-104	351	7	1	1	NUM
ma-104	351	8	.	.	PUNCT
ma-104	352	1	introduction	introduction	NOUN
ma-104	352	2	2	2	NUM
ma-104	352	3	.	.	PUNCT
ma-104	352	4	majorization	majorization	NOUN
ma-104	352	5	of	of	ADP
ma-104	352	6	ni	ni	PROPN
ma-104	352	7	3	3	PROPN
ma-104	352	8	.	.	PUNCT
ma-104	352	9	convergence	convergence	NOUN
ma-104	352	10	of	of	ADP
ma-104	352	11	nm	nm	ADJ
ma-104	352	12	4	4	NUM
ma-104	352	13	.	.	PUNCT
ma-104	352	14	numerical	numerical	ADJ
ma-104	352	15	experimentation	experimentation	NOUN
ma-104	352	16	5	5	NUM
ma-104	352	17	.	.	PUNCT
ma-104	353	1	conclusions	conclusion	NOUN
ma-104	353	2	references	reference	NOUN