id	sid	tid	token	lemma	pos
ma-207	1	1	2024	2024	NUM
ma-207	1	2	ada	ada	PROPN
ma-207	1	3	academica	academica	PROPN
ma-207	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-207	1	5	.	.	PUNCT
ma-207	2	1	j.	j.	PROPN
ma-207	2	2	math	math	PROPN
ma-207	2	3	.	.	PUNCT
ma-207	3	1	anal	anal	ADJ
ma-207	3	2	.	.	PUNCT
ma-207	4	1	4	4	NUM
ma-207	4	2	(	(	PUNCT
ma-207	4	3	2024	2024	NUM
ma-207	4	4	)	)	PUNCT
ma-207	5	1	3doi	3doi	NUM
ma-207	5	2	:	:	PUNCT
ma-207	5	3	10.28924	10.28924	NUM
ma-207	5	4	/	/	SYM
ma-207	5	5	ada	ada	PROPN
ma-207	5	6	/	/	PROPN
ma-207	5	7	ma.4.3	ma.4.3	VERB
ma-207	5	8	a	a	DET
ma-207	5	9	unified	unified	ADJ
ma-207	5	10	kantorovich	kantorovich	NOUN
ma-207	5	11	-	-	PUNCT
ma-207	5	12	type	type	NOUN
ma-207	5	13	convergence	convergence	NOUN
ma-207	5	14	analysis	analysis	NOUN
ma-207	5	15	of	of	ADP
ma-207	5	16	newton	newton	PROPN
ma-207	5	17	-	-	PUNCT
ma-207	5	18	like	like	ADJ
ma-207	5	19	methods	method	NOUN
ma-207	5	20	for	for	ADP
ma-207	5	21	solving	solve	VERB
ma-207	5	22	generalized	generalized	ADJ
ma-207	5	23	equations	equation	NOUN
ma-207	5	24	under	under	ADP
ma-207	5	25	the	the	DET
ma-207	5	26	aubin	aubin	PROPN
ma-207	5	27	property	property	NOUN
ma-207	5	28	samundra	samundra	NOUN
ma-207	5	29	regmi1	regmi1	PROPN
ma-207	5	30	,	,	PUNCT
ma-207	5	31	ioannis	ioannis	PROPN
ma-207	5	32	k.	k.	PROPN
ma-207	5	33	argyros2,∗	argyros2,∗	PROPN
ma-207	5	34	,	,	PUNCT
ma-207	5	35	santhosh	santhosh	PROPN
ma-207	5	36	george3	george3	PROPN
ma-207	5	37	,	,	PUNCT
ma-207	5	38	and	and	CCONJ
ma-207	5	39	jefferey	jefferey	PROPN
ma-207	5	40	warden2	warden2	VERB
ma-207	5	41	1department	1department	NUM
ma-207	5	42	of	of	ADP
ma-207	5	43	mathematics	mathematic	NOUN
ma-207	5	44	,	,	PUNCT
ma-207	5	45	university	university	PROPN
ma-207	5	46	of	of	ADP
ma-207	5	47	houston	houston	PROPN
ma-207	5	48	,	,	PUNCT
ma-207	5	49	houston	houston	PROPN
ma-207	5	50	,	,	PUNCT
ma-207	5	51	tx	tx	PROPN
ma-207	5	52	,	,	PUNCT
ma-207	5	53	77024	77024	NUM
ma-207	5	54	,	,	PUNCT
ma-207	6	1	usa	usa	PROPN
ma-207	6	2	sregmi5@uh.edu	sregmi5@uh.edu	PROPN
ma-207	6	3	2department	2department	NUM
ma-207	6	4	of	of	ADP
ma-207	6	5	computing	computing	NOUN
ma-207	6	6	and	and	CCONJ
ma-207	6	7	mathematical	mathematical	ADJ
ma-207	6	8	sciences	sciences	PROPN
ma-207	6	9	,	,	PUNCT
ma-207	6	10	cameron	cameron	PROPN
ma-207	6	11	university	university	PROPN
ma-207	6	12	,	,	PUNCT
ma-207	6	13	lawton	lawton	PROPN
ma-207	6	14	,	,	PUNCT
ma-207	6	15	ok	ok	PROPN
ma-207	6	16	73505	73505	NUM
ma-207	6	17	,	,	PUNCT
ma-207	6	18	usa	usa	PROPN
ma-207	6	19	iargyros@cameron.edu	iargyros@cameron.edu	PROPN
ma-207	6	20	,	,	PUNCT
ma-207	6	21	jefferey.warden@cameron.edu	jefferey.warden@cameron.edu	PROPN
ma-207	6	22	3department	3department	NUM
ma-207	6	23	of	of	ADP
ma-207	6	24	mathematical	mathematical	ADJ
ma-207	6	25	and	and	CCONJ
ma-207	6	26	computational	computational	ADJ
ma-207	6	27	sciences	science	NOUN
ma-207	6	28	,	,	PUNCT
ma-207	6	29	national	national	PROPN
ma-207	6	30	institute	institute	PROPN
ma-207	6	31	of	of	ADP
ma-207	6	32	technology	technology	PROPN
ma-207	6	33	karnataka	karnataka	PROPN
ma-207	6	34	,	,	PUNCT
ma-207	6	35	india-575	india-575	ADJ
ma-207	6	36	025	025	NUM
ma-207	6	37	sgeorge@nitk.edu.in	sgeorge@nitk.edu.in	NOUN
ma-207	6	38	∗correspondence	∗correspondence	NOUN
ma-207	6	39	:	:	PUNCT
ma-207	6	40	iargyros@cameron.edu	iargyros@cameron.edu	X
ma-207	7	1	abstract	abstract	ADJ
ma-207	7	2	.	.	PUNCT
ma-207	8	1	numerous	numerous	ADJ
ma-207	8	2	applications	application	NOUN
ma-207	8	3	from	from	ADP
ma-207	8	4	diverse	diverse	ADJ
ma-207	8	5	disciplines	discipline	NOUN
ma-207	8	6	reduce	reduce	VERB
ma-207	8	7	to	to	ADP
ma-207	8	8	solving	solve	VERB
ma-207	8	9	generalized	generalized	ADJ
ma-207	8	10	equationsin	equationsin	NOUN
ma-207	8	11	a	a	DET
ma-207	8	12	banach	banach	NOUN
ma-207	8	13	space	space	NOUN
ma-207	8	14	setting	setting	NOUN
ma-207	8	15	.	.	PUNCT
ma-207	9	1	these	these	DET
ma-207	9	2	equations	equation	NOUN
ma-207	9	3	are	be	AUX
ma-207	9	4	solved	solve	VERB
ma-207	9	5	mostly	mostly	ADV
ma-207	9	6	iteratively	iteratively	ADV
ma-207	9	7	,	,	PUNCT
ma-207	9	8	when	when	SCONJ
ma-207	9	9	a	a	DET
ma-207	9	10	sequence	sequence	NOUN
ma-207	9	11	is	be	AUX
ma-207	9	12	gen	gen	ADJ
ma-207	9	13	-	-	ADJ
ma-207	9	14	erated	erated	ADJ
ma-207	9	15	approximating	approximate	VERB
ma-207	9	16	a	a	DET
ma-207	9	17	solution	solution	NOUN
ma-207	9	18	provided	provide	VERB
ma-207	9	19	that	that	SCONJ
ma-207	9	20	certain	certain	ADJ
ma-207	9	21	conditions	condition	NOUN
ma-207	9	22	are	be	AUX
ma-207	9	23	valid	valid	ADJ
ma-207	9	24	on	on	ADP
ma-207	9	25	the	the	DET
ma-207	9	26	starting	starting	NOUN
ma-207	9	27	point	point	NOUN
ma-207	9	28	andthe	andthe	ADJ
ma-207	9	29	operators	operator	NOUN
ma-207	9	30	appearing	appear	VERB
ma-207	9	31	on	on	ADP
ma-207	9	32	the	the	DET
ma-207	9	33	method	method	NOUN
ma-207	9	34	.	.	PUNCT
ma-207	10	1	in	in	ADP
ma-207	10	2	particular	particular	ADJ
ma-207	10	3	,	,	PUNCT
ma-207	10	4	newton	newton	PROPN
ma-207	10	5	-	-	PUNCT
ma-207	10	6	like	like	ADJ
ma-207	10	7	methods	method	NOUN
ma-207	10	8	are	be	AUX
ma-207	10	9	developed	develop	VERB
ma-207	10	10	whosespecializations	whosespecialization	NOUN
ma-207	10	11	reduce	reduce	VERB
ma-207	10	12	to	to	ADP
ma-207	10	13	well	well	ADV
ma-207	10	14	known	know	VERB
ma-207	10	15	methods	method	NOUN
ma-207	10	16	such	such	ADJ
ma-207	10	17	as	as	ADP
ma-207	10	18	newton	newton	PROPN
ma-207	10	19	,	,	PUNCT
ma-207	10	20	modified	modified	PROPN
ma-207	10	21	newton	newton	PROPN
ma-207	10	22	,	,	PUNCT
ma-207	10	23	secant	secant	PROPN
ma-207	10	24	,	,	PUNCT
ma-207	10	25	kurchatovand	kurchatovand	PROPN
ma-207	10	26	steffensen	steffensen	NOUN
ma-207	10	27	to	to	PART
ma-207	10	28	mention	mention	VERB
ma-207	10	29	a	a	DET
ma-207	10	30	few	few	ADJ
ma-207	10	31	.	.	PUNCT
ma-207	11	1	a	a	DET
ma-207	11	2	unified	unified	ADJ
ma-207	11	3	semi	semi	ADJ
ma-207	11	4	-	-	ADJ
ma-207	11	5	local	local	ADJ
ma-207	11	6	analysis	analysis	NOUN
ma-207	11	7	of	of	ADP
ma-207	11	8	these	these	DET
ma-207	11	9	methods	method	NOUN
ma-207	11	10	is	be	AUX
ma-207	11	11	presented	present	VERB
ma-207	11	12	usingthe	usingthe	DET
ma-207	11	13	contraction	contraction	NOUN
ma-207	11	14	mapping	mapping	NOUN
ma-207	11	15	principle	principle	NOUN
ma-207	11	16	under	under	ADP
ma-207	11	17	the	the	DET
ma-207	11	18	aubin	aubin	PROPN
ma-207	11	19	property	property	NOUN
ma-207	11	20	of	of	ADP
ma-207	11	21	a	a	DET
ma-207	11	22	set	set	NOUN
ma-207	11	23	valued	value	VERB
ma-207	11	24	operator	operator	NOUN
ma-207	11	25	,	,	PUNCT
ma-207	11	26	and	and	CCONJ
ma-207	11	27	generalizedcontinuity	generalizedcontinuity	NOUN
ma-207	11	28	assumption	assumption	NOUN
ma-207	11	29	on	on	ADP
ma-207	11	30	the	the	DET
ma-207	11	31	operators	operator	NOUN
ma-207	11	32	on	on	ADP
ma-207	11	33	these	these	DET
ma-207	11	34	methods	method	NOUN
ma-207	11	35	.	.	PUNCT
ma-207	12	1	1	1	X
ma-207	12	2	.	.	X
ma-207	12	3	introduction	introduction	NOUN
ma-207	12	4	let	let	VERB
ma-207	12	5	b1	b1	NOUN
ma-207	12	6	and	and	CCONJ
ma-207	12	7	b2	b2	NOUN
ma-207	12	8	stand	stand	NOUN
ma-207	12	9	for	for	ADP
ma-207	12	10	complete	complete	ADJ
ma-207	12	11	normed	normed	ADJ
ma-207	12	12	spaces	space	NOUN
ma-207	12	13	;	;	PUNCT
ma-207	12	14	d	d	X
ma-207	12	15	be	be	AUX
ma-207	12	16	an	an	DET
ma-207	12	17	open	open	ADJ
ma-207	12	18	and	and	CCONJ
ma-207	12	19	convex	convex	NOUN
ma-207	12	20	subset	subset	NOUN
ma-207	12	21	of	of	ADP
ma-207	12	22	b1;operator	b1;operator	NOUN
ma-207	12	23	f	f	NOUN
ma-207	12	24	:	:	PUNCT
ma-207	12	25	d	d	SCONJ
ma-207	12	26	−→	−→	NOUN
ma-207	12	27	b2	b2	NOUN
ma-207	12	28	be	be	AUX
ma-207	12	29	continuous	continuous	ADJ
ma-207	12	30	and	and	CCONJ
ma-207	12	31	g	g	NOUN
ma-207	12	32	:	:	PUNCT
ma-207	12	33	b1	b1	PROPN
ma-207	12	34	⇒	⇒	PROPN
ma-207	12	35	b2	b2	NOUN
ma-207	12	36	be	be	AUX
ma-207	12	37	a	a	DET
ma-207	12	38	set	set	NOUN
ma-207	12	39	-	-	PUNCT
ma-207	12	40	valued	value	VERB
ma-207	12	41	operator	operator	NOUN
ma-207	12	42	with	with	ADP
ma-207	12	43	closedgraph	closedgraph	NOUN
ma-207	12	44	,	,	PUNCT
ma-207	12	45	which	which	PRON
ma-207	12	46	is	be	AUX
ma-207	12	47	a	a	DET
ma-207	12	48	nonempty	nonempty	ADJ
ma-207	12	49	set	set	NOUN
ma-207	12	50	[	[	PUNCT
ma-207	12	51	15].we	15].we	NUM
ma-207	12	52	are	be	AUX
ma-207	12	53	concerned	concern	VERB
ma-207	12	54	with	with	ADP
ma-207	12	55	the	the	DET
ma-207	12	56	problem	problem	NOUN
ma-207	12	57	of	of	ADP
ma-207	12	58	finding	find	VERB
ma-207	12	59	a	a	DET
ma-207	12	60	solution	solution	NOUN
ma-207	12	61	x∗	x∗	PROPN
ma-207	12	62	∈	∈	PROPN
ma-207	12	63	b1	b1	NOUN
ma-207	12	64	of	of	ADP
ma-207	12	65	the	the	DET
ma-207	12	66	generalized	generalize	VERB
ma-207	12	67	equationiteratively	equationiteratively	NOUN
ma-207	12	68	in	in	ADP
ma-207	12	69	the	the	DET
ma-207	12	70	form	form	NOUN
ma-207	12	71	:	:	PUNCT
ma-207	12	72	find	find	VERB
ma-207	12	73	x	x	X
ma-207	12	74	∈	∈	NOUN
ma-207	12	75	b1	b1	NOUN
ma-207	13	1	so	so	SCONJ
ma-207	13	2	that	that	SCONJ
ma-207	13	3	f	f	X
ma-207	13	4	(	(	PUNCT
ma-207	13	5	x	x	X
ma-207	13	6	)	)	PUNCT
ma-207	13	7	+	+	CCONJ
ma-207	13	8	g(x	g(x	NOUN
ma-207	13	9	)	)	PUNCT
ma-207	13	10	3	3	NUM
ma-207	13	11	0	0	NUM
ma-207	13	12	.	.	PUNCT
ma-207	13	13	(	(	PUNCT
ma-207	13	14	1.1	1.1	NUM
ma-207	13	15	)	)	PUNCT
ma-207	13	16	many	many	ADJ
ma-207	13	17	applications	application	NOUN
ma-207	13	18	from	from	ADP
ma-207	13	19	diverse	diverse	ADJ
ma-207	13	20	disciplines	discipline	NOUN
ma-207	13	21	,	,	PUNCT
ma-207	13	22	especially	especially	ADV
ma-207	13	23	in	in	ADP
ma-207	13	24	mathematical	mathematical	ADJ
ma-207	13	25	programming	programming	NOUN
ma-207	13	26	can	can	AUX
ma-207	13	27	be	be	AUX
ma-207	13	28	for	for	ADP
ma-207	13	29	-	-	PUNCT
ma-207	13	30	mulated	mulate	VERB
ma-207	13	31	like	like	ADP
ma-207	13	32	the	the	DET
ma-207	13	33	generalized	generalized	ADJ
ma-207	13	34	equation	equation	NOUN
ma-207	13	35	(	(	PUNCT
ma-207	13	36	1.1	1.1	NUM
ma-207	13	37	)	)	PUNCT
ma-207	14	1	[	[	X
ma-207	14	2	1–15	1–15	NUM
ma-207	14	3	,	,	PUNCT
ma-207	14	4	23–25	23–25	NUM
ma-207	14	5	,	,	PUNCT
ma-207	14	6	34	34	NUM
ma-207	14	7	]	]	PUNCT
ma-207	14	8	.	.	PUNCT
ma-207	15	1	s.	s.	PROPN
ma-207	15	2	m.	m.	PROPN
ma-207	15	3	robinson	robinson	PROPN
ma-207	15	4	inaugurated	inaugurate	VERB
ma-207	15	5	the	the	DET
ma-207	15	6	received	received	NOUN
ma-207	15	7	:	:	PUNCT
ma-207	15	8	26	26	NUM
ma-207	15	9	dec	dec	PROPN
ma-207	15	10	2023	2023	NUM
ma-207	15	11	.	.	PUNCT
ma-207	16	1	key	key	ADJ
ma-207	16	2	words	word	NOUN
ma-207	16	3	and	and	CCONJ
ma-207	16	4	phrases	phrase	NOUN
ma-207	16	5	.	.	PUNCT
ma-207	17	1	generalized	generalized	ADJ
ma-207	17	2	equation	equation	NOUN
ma-207	17	3	;	;	PUNCT
ma-207	17	4	newton	newton	PROPN
ma-207	17	5	-	-	PUNCT
ma-207	17	6	like	like	ADJ
ma-207	17	7	methods	method	NOUN
ma-207	17	8	;	;	PUNCT
ma-207	17	9	aubin	aubin	PROPN
ma-207	17	10	property	property	NOUN
ma-207	17	11	;	;	PUNCT
ma-207	17	12	banach	banach	NOUN
ma-207	17	13	space	space	NOUN
ma-207	17	14	;	;	PUNCT
ma-207	17	15	local	local	ADJ
ma-207	17	16	-	-	PUNCT
ma-207	17	17	semi	semi	ADJ
ma-207	17	18	-	-	ADJ
ma-207	17	19	local	local	ADJ
ma-207	17	20	convergence	convergence	NOUN
ma-207	17	21	;	;	PUNCT
ma-207	17	22	newton	newton	PROPN
ma-207	17	23	’s	’s	PART
ma-207	17	24	method	method	NOUN
ma-207	17	25	.	.	PUNCT
ma-207	18	1	1	1	NUM
ma-207	18	2	https://adac.ee	https://adac.ee	PROPN
ma-207	18	3	https://doi.org/10.28924/ada/ma.4.3	https://doi.org/10.28924/ada/ma.4.3	PROPN
ma-207	18	4	eur	eur	PROPN
ma-207	18	5	.	.	PUNCT
ma-207	19	1	j.	j.	PROPN
ma-207	19	2	math	math	PROPN
ma-207	19	3	.	.	PUNCT
ma-207	20	1	anal	anal	PROPN
ma-207	20	2	.	.	PUNCT
ma-207	21	1	10.28924	10.28924	NUM
ma-207	21	2	/	/	SYM
ma-207	21	3	ada	ada	PROPN
ma-207	21	4	/	/	SYM
ma-207	21	5	ma.4.3	ma.4.3	PROPN
ma-207	21	6	2study	2study	NUM
ma-207	21	7	of	of	ADP
ma-207	21	8	generalized	generalized	ADJ
ma-207	21	9	equations	equation	NOUN
ma-207	21	10	in	in	ADP
ma-207	21	11	[	[	X
ma-207	21	12	23–25	23–25	NUM
ma-207	21	13	]	]	PUNCT
ma-207	21	14	.	.	PUNCT
ma-207	22	1	a	a	DET
ma-207	22	2	solution	solution	NOUN
ma-207	22	3	x∗	x∗	PROPN
ma-207	22	4	∈	∈	PROPN
ma-207	22	5	b1	b1	NOUN
ma-207	22	6	in	in	ADP
ma-207	22	7	analytical	analytical	ADJ
ma-207	22	8	form	form	NOUN
ma-207	22	9	or	or	CCONJ
ma-207	22	10	closed	close	VERB
ma-207	22	11	form	form	NOUN
ma-207	22	12	iscomputationally	iscomputationally	ADV
ma-207	22	13	hard	hard	ADJ
ma-207	22	14	or	or	CCONJ
ma-207	22	15	impossible	impossible	ADJ
ma-207	22	16	to	to	PART
ma-207	22	17	find	find	VERB
ma-207	22	18	.	.	PUNCT
ma-207	23	1	thus	thus	ADV
ma-207	23	2	,	,	PUNCT
ma-207	23	3	researchers	researcher	NOUN
ma-207	23	4	and	and	CCONJ
ma-207	23	5	practitioners	practitioner	NOUN
ma-207	23	6	generate	generate	VERB
ma-207	23	7	iterativemethods	iterativemethod	NOUN
ma-207	23	8	approximating	approximate	VERB
ma-207	23	9	x∗	x∗	PROPN
ma-207	23	10	if	if	SCONJ
ma-207	23	11	certain	certain	ADJ
ma-207	23	12	conditions	condition	NOUN
ma-207	23	13	related	relate	VERB
ma-207	23	14	to	to	ADP
ma-207	23	15	the	the	DET
ma-207	23	16	starting	starting	NOUN
ma-207	23	17	point	point	NOUN
ma-207	23	18	and	and	CCONJ
ma-207	23	19	the	the	DET
ma-207	23	20	operators	operator	NOUN
ma-207	23	21	onthe	onthe	NOUN
ma-207	23	22	methods	method	NOUN
ma-207	23	23	are	be	AUX
ma-207	23	24	fulfilled	fulfil	VERB
ma-207	23	25	.	.	PUNCT
ma-207	24	1	n	n	X
ma-207	24	2	,	,	PUNCT
ma-207	24	3	h.	h.	PROPN
ma-207	24	4	josephy	josephy	PROPN
ma-207	24	5	introduced	introduce	VERB
ma-207	24	6	the	the	DET
ma-207	24	7	newton	newton	PROPN
ma-207	24	8	method	method	NOUN
ma-207	24	9	for	for	ADP
ma-207	24	10	solving	solve	VERB
ma-207	24	11	the	the	DET
ma-207	24	12	generalizedequation	generalizedequation	NOUN
ma-207	24	13	(	(	PUNCT
ma-207	24	14	1.1	1.1	NUM
ma-207	24	15	)	)	PUNCT
ma-207	24	16	in	in	ADP
ma-207	24	17	[	[	X
ma-207	24	18	18	18	NUM
ma-207	24	19	]	]	PUNCT
ma-207	24	20	.	.	PUNCT
ma-207	25	1	later	later	ADV
ma-207	25	2	,	,	PUNCT
ma-207	25	3	numerous	numerous	ADJ
ma-207	25	4	other	other	ADJ
ma-207	25	5	authors	author	NOUN
ma-207	25	6	worked	work	VERB
ma-207	25	7	on	on	ADP
ma-207	25	8	various	various	ADJ
ma-207	25	9	other	other	ADJ
ma-207	25	10	iterative	iterative	NOUN
ma-207	25	11	methodsunder	methodsunder	NOUN
ma-207	25	12	diverse	diverse	ADJ
ma-207	25	13	convergence	convergence	NOUN
ma-207	25	14	conditions	condition	NOUN
ma-207	25	15	(	(	PUNCT
ma-207	25	16	see	see	VERB
ma-207	25	17	[	[	X
ma-207	25	18	1–3,7–15	1–3,7–15	NUM
ma-207	25	19	]	]	PUNCT
ma-207	25	20	and	and	CCONJ
ma-207	25	21	references	reference	NOUN
ma-207	25	22	there	there	ADV
ma-207	25	23	in).all	in).all	NOUN
ma-207	25	24	these	these	DET
ma-207	25	25	iterative	iterative	NOUN
ma-207	25	26	methods	method	NOUN
ma-207	25	27	are	be	AUX
ma-207	25	28	useful	useful	ADJ
ma-207	25	29	and	and	CCONJ
ma-207	25	30	provide	provide	VERB
ma-207	25	31	insight	insight	NOUN
ma-207	25	32	in	in	ADP
ma-207	25	33	the	the	DET
ma-207	25	34	solutions	solution	NOUN
ma-207	25	35	of	of	ADP
ma-207	25	36	generalized	generalized	ADJ
ma-207	25	37	equa	equa	NOUN
ma-207	25	38	-	-	PUNCT
ma-207	25	39	tions	tion	NOUN
ma-207	25	40	.	.	PUNCT
ma-207	26	1	but	but	CCONJ
ma-207	26	2	as	as	ADV
ma-207	26	3	far	far	ADV
ma-207	26	4	as	as	SCONJ
ma-207	26	5	we	we	PRON
ma-207	26	6	know	know	VERB
ma-207	26	7	there	there	PRON
ma-207	26	8	is	be	VERB
ma-207	26	9	not	not	PART
ma-207	26	10	a	a	DET
ma-207	26	11	unified	unified	ADJ
ma-207	26	12	convergence	convergence	NOUN
ma-207	26	13	analysis	analysis	NOUN
ma-207	26	14	for	for	ADP
ma-207	26	15	the	the	DET
ma-207	26	16	existing	exist	VERB
ma-207	26	17	iterativemethods	iterativemethod	NOUN
ma-207	26	18	.	.	PUNCT
ma-207	27	1	that	that	PRON
ma-207	27	2	is	be	AUX
ma-207	27	3	very	very	ADV
ma-207	27	4	useful	useful	ADJ
ma-207	27	5	,	,	PUNCT
ma-207	27	6	since	since	SCONJ
ma-207	27	7	this	this	DET
ma-207	27	8	way	way	NOUN
ma-207	27	9	under	under	ADP
ma-207	27	10	the	the	DET
ma-207	27	11	same	same	ADJ
ma-207	27	12	set	set	NOUN
ma-207	27	13	of	of	ADP
ma-207	27	14	conditions	condition	NOUN
ma-207	27	15	the	the	DET
ma-207	27	16	convergence	convergence	NOUN
ma-207	27	17	andcomparison	andcomparison	NOUN
ma-207	27	18	of	of	ADP
ma-207	27	19	numerous	numerous	ADJ
ma-207	27	20	iterative	iterative	NOUN
ma-207	27	21	methods	method	NOUN
ma-207	27	22	becomes	become	VERB
ma-207	27	23	possible	possible	ADJ
ma-207	27	24	.	.	PUNCT
ma-207	28	1	this	this	PRON
ma-207	28	2	is	be	AUX
ma-207	28	3	our	our	PRON
ma-207	28	4	motivation	motivation	NOUN
ma-207	28	5	for	for	ADP
ma-207	28	6	the	the	DET
ma-207	28	7	presentarticle	presentarticle	NOUN
ma-207	28	8	.	.	PUNCT
ma-207	29	1	in	in	ADP
ma-207	29	2	particular	particular	ADJ
ma-207	29	3	,	,	PUNCT
ma-207	29	4	consider	consider	VERB
ma-207	29	5	the	the	DET
ma-207	29	6	newton	newton	NOUN
ma-207	29	7	-	-	PUNCT
ma-207	29	8	like	like	ADJ
ma-207	29	9	iterative	iterative	NOUN
ma-207	29	10	method	method	NOUN
ma-207	29	11	(	(	PUNCT
ma-207	29	12	nlm	nlm	PROPN
ma-207	29	13	)	)	PUNCT
ma-207	29	14	for	for	ADP
ma-207	29	15	solving	solve	VERB
ma-207	29	16	the	the	DET
ma-207	29	17	generalizedequation	generalizedequation	NOUN
ma-207	29	18	in	in	ADP
ma-207	29	19	the	the	DET
ma-207	29	20	following	follow	VERB
ma-207	29	21	form	form	NOUN
ma-207	29	22	f	f	PROPN
ma-207	29	23	(	(	PUNCT
ma-207	29	24	xn	xn	PROPN
ma-207	29	25	)	)	PUNCT
ma-207	29	26	+	+	CCONJ
ma-207	29	27	l(xn)(xn+1	l(xn)(xn+1	VERB
ma-207	29	28	−	−	PROPN
ma-207	29	29	xn	xn	PROPN
ma-207	29	30	)	)	PUNCT
ma-207	30	1	+	+	CCONJ
ma-207	30	2	g(xn+1	g(xn+1	NOUN
ma-207	30	3	)	)	PUNCT
ma-207	30	4	3	3	NUM
ma-207	30	5	0	0	NUM
ma-207	30	6	,	,	PUNCT
ma-207	30	7	n	n	NOUN
ma-207	30	8	=	=	SYM
ma-207	30	9	0	0	NUM
ma-207	30	10	,	,	PUNCT
ma-207	30	11	1	1	NUM
ma-207	30	12	,	,	PUNCT
ma-207	30	13	2	2	NUM
ma-207	30	14	,	,	PUNCT
ma-207	30	15	.	.	PUNCT
ma-207	30	16	.	.	PUNCT
ma-207	30	17	.	.	PUNCT
ma-207	31	1	,	,	PUNCT
ma-207	31	2	(	(	PUNCT
ma-207	31	3	1.2	1.2	NUM
ma-207	31	4	)	)	PUNCT
ma-207	31	5	where	where	SCONJ
ma-207	31	6	l	l	NOUN
ma-207	31	7	(	(	PUNCT
ma-207	31	8	.	.	PUNCT
ma-207	31	9	)	)	PUNCT
ma-207	31	10	:	:	PUNCT
ma-207	31	11	b1	b1	VERB
ma-207	31	12	−→	−→	ADJ
ma-207	31	13	l(b1	l(b1	NOUN
ma-207	31	14	,	,	PUNCT
ma-207	31	15	b2	b2	PROPN
ma-207	31	16	)	)	PUNCT
ma-207	31	17	which	which	PRON
ma-207	31	18	stands	stand	VERB
ma-207	31	19	for	for	ADP
ma-207	31	20	the	the	DET
ma-207	31	21	space	space	NOUN
ma-207	31	22	of	of	ADP
ma-207	31	23	linear	linear	PROPN
ma-207	31	24	operators	operator	NOUN
ma-207	31	25	which	which	PRON
ma-207	31	26	are	be	AUX
ma-207	31	27	boundedmapping	boundedmappe	VERB
ma-207	31	28	from	from	ADP
ma-207	31	29	b1	b1	NOUN
ma-207	31	30	into	into	ADP
ma-207	31	31	b2	b2	NOUN
ma-207	31	32	.	.	PUNCT
ma-207	32	1	by	by	ADP
ma-207	32	2	specializing	specialize	VERB
ma-207	32	3	the	the	DET
ma-207	32	4	linear	linear	ADJ
ma-207	32	5	operator	operator	NOUN
ma-207	32	6	l	l	NOUN
ma-207	32	7	,	,	PUNCT
ma-207	32	8	many	many	ADJ
ma-207	32	9	iterative	iterative	NOUN
ma-207	32	10	methods	method	NOUN
ma-207	32	11	can	can	AUX
ma-207	32	12	beobtained	beobtaine	VERB
ma-207	32	13	such	such	ADJ
ma-207	32	14	as	as	ADP
ma-207	32	15	:	:	PUNCT
ma-207	32	16	newton	newton	PROPN
ma-207	32	17	’s	’s	PART
ma-207	32	18	method	method	NOUN
ma-207	33	1	[	[	X
ma-207	33	2	4,5,21,22	4,5,21,22	PROPN
ma-207	33	3	]	]	X
ma-207	33	4	:	:	PUNCT
ma-207	33	5	select	select	ADJ
ma-207	33	6	l(x	l(x	PROPN
ma-207	33	7	)	)	PUNCT
ma-207	33	8	=	=	SYM
ma-207	33	9	f	f	NOUN
ma-207	33	10	′(x	′(x	PROPN
ma-207	33	11	)	)	PUNCT
ma-207	33	12	,	,	PUNCT
ma-207	33	13	x	x	PUNCT
ma-207	33	14	∈	∈	NOUN
ma-207	33	15	b1	b1	NOUN
ma-207	33	16	to	to	PART
ma-207	33	17	obtain	obtain	VERB
ma-207	33	18	f	f	PROPN
ma-207	33	19	(	(	PUNCT
ma-207	33	20	xn	xn	PROPN
ma-207	33	21	)	)	PUNCT
ma-207	34	1	+	+	CCONJ
ma-207	34	2	f	f	X
ma-207	34	3	′(xn)(xn+1	′(xn)(xn+1	PROPN
ma-207	34	4	−	−	PROPN
ma-207	34	5	xn	xn	NUM
ma-207	34	6	)	)	PUNCT
ma-207	35	1	+	+	CCONJ
ma-207	35	2	g(xn+1	g(xn+1	NOUN
ma-207	35	3	)	)	PUNCT
ma-207	35	4	3	3	NUM
ma-207	35	5	0	0	NUM
ma-207	35	6	,	,	PUNCT
ma-207	35	7	n	n	NOUN
ma-207	35	8	=	=	SYM
ma-207	35	9	0	0	NUM
ma-207	35	10	,	,	PUNCT
ma-207	35	11	1	1	NUM
ma-207	35	12	,	,	PUNCT
ma-207	35	13	2	2	NUM
ma-207	35	14	,	,	PUNCT
ma-207	35	15	.	.	PUNCT
ma-207	35	16	.	.	PUNCT
ma-207	35	17	.	.	PUNCT
ma-207	36	1	,	,	PUNCT
ma-207	36	2	where	where	SCONJ
ma-207	36	3	f	f	PROPN
ma-207	36	4	′	′	NOUN
ma-207	36	5	denotes	denote	VERB
ma-207	36	6	the	the	DET
ma-207	36	7	derivative	derivative	NOUN
ma-207	36	8	according	accord	VERB
ma-207	36	9	to	to	ADP
ma-207	36	10	fréchet	fréchet	NOUN
ma-207	36	11	of	of	ADP
ma-207	36	12	the	the	DET
ma-207	36	13	operator	operator	NOUN
ma-207	36	14	f.	f.	PROPN
ma-207	36	15	modified	modified	PROPN
ma-207	36	16	newton	newton	PROPN
ma-207	36	17	’s	’s	PART
ma-207	36	18	method	method	NOUN
ma-207	37	1	[	[	X
ma-207	37	2	4,5,20	4,5,20	NUM
ma-207	37	3	]	]	X
ma-207	37	4	:	:	PUNCT
ma-207	37	5	set	set	VERB
ma-207	37	6	l(x	l(x	PROPN
ma-207	37	7	)	)	PUNCT
ma-207	38	1	=	=	SYM
ma-207	38	2	f	f	PROPN
ma-207	38	3	′(x0	′(x0	NOUN
ma-207	38	4	)	)	PUNCT
ma-207	38	5	,	,	PUNCT
ma-207	38	6	x	x	PUNCT
ma-207	38	7	∈	∈	NOUN
ma-207	38	8	b1	b1	NOUN
ma-207	38	9	to	to	PART
ma-207	38	10	obtain	obtain	VERB
ma-207	38	11	f	f	PROPN
ma-207	38	12	(	(	PUNCT
ma-207	38	13	xn	xn	PROPN
ma-207	38	14	)	)	PUNCT
ma-207	39	1	+	+	CCONJ
ma-207	39	2	f	f	PROPN
ma-207	39	3	′(x0)(xn+1	′(x0)(xn+1	PROPN
ma-207	39	4	−	−	PROPN
ma-207	39	5	xn	xn	NUM
ma-207	39	6	)	)	PUNCT
ma-207	39	7	+	+	CCONJ
ma-207	39	8	g(xn+1	g(xn+1	NOUN
ma-207	39	9	)	)	PUNCT
ma-207	39	10	3	3	NUM
ma-207	39	11	0	0	NUM
ma-207	39	12	,	,	PUNCT
ma-207	39	13	n	n	NOUN
ma-207	39	14	=	=	SYM
ma-207	39	15	0	0	NUM
ma-207	39	16	,	,	PUNCT
ma-207	39	17	1	1	NUM
ma-207	39	18	,	,	PUNCT
ma-207	39	19	2	2	NUM
ma-207	39	20	,	,	PUNCT
ma-207	39	21	.	.	PUNCT
ma-207	39	22	.	.	PUNCT
ma-207	39	23	.	.	PUNCT
ma-207	39	24	.	.	PUNCT
ma-207	40	1	secant	secant	ADJ
ma-207	40	2	method	method	NOUN
ma-207	40	3	[	[	X
ma-207	40	4	20	20	NUM
ma-207	40	5	]	]	PUNCT
ma-207	40	6	:	:	PUNCT
ma-207	40	7	let	let	VERB
ma-207	40	8	l(xn	l(xn	NOUN
ma-207	40	9	)	)	PUNCT
ma-207	40	10	=	=	PUNCT
ma-207	41	1	[	[	X
ma-207	41	2	xn−1	xn−1	PROPN
ma-207	41	3	,	,	PUNCT
ma-207	41	4	xn;f	xn;f	PUNCT
ma-207	41	5	]	]	PUNCT
ma-207	41	6	,	,	PUNCT
ma-207	41	7	n	n	PROPN
ma-207	41	8	=	=	SYM
ma-207	41	9	0	0	NUM
ma-207	41	10	,	,	PUNCT
ma-207	41	11	1	1	NUM
ma-207	41	12	,	,	PUNCT
ma-207	41	13	2	2	NUM
ma-207	41	14	,	,	PUNCT
ma-207	41	15	.	.	PUNCT
ma-207	41	16	.	.	PUNCT
ma-207	41	17	.	.	PUNCT
ma-207	42	1	a	a	DET
ma-207	42	2	divided	divide	VERB
ma-207	42	3	difference	difference	NOUN
ma-207	42	4	of	of	ADP
ma-207	42	5	order	order	NOUN
ma-207	42	6	one	one	NUM
ma-207	43	1	[	[	X
ma-207	43	2	20].then	20].then	PROPN
ma-207	43	3	,	,	PUNCT
ma-207	43	4	iterative	iterative	NOUN
ma-207	43	5	method	method	NOUN
ma-207	43	6	(	(	PUNCT
ma-207	43	7	1.1	1.1	NUM
ma-207	43	8	)	)	PUNCT
ma-207	43	9	becomes	become	VERB
ma-207	43	10	f	f	PROPN
ma-207	43	11	(	(	PUNCT
ma-207	43	12	xn	xn	PROPN
ma-207	43	13	)	)	PUNCT
ma-207	44	1	+	+	CCONJ
ma-207	45	1	[	[	X
ma-207	45	2	xn−1	xn−1	PROPN
ma-207	45	3	,	,	PUNCT
ma-207	45	4	xn;f	xn;f	PUNCT
ma-207	45	5	]	]	PUNCT
ma-207	45	6	(	(	PUNCT
ma-207	45	7	xn+1	xn+1	NUM
ma-207	45	8	−	−	NOUN
ma-207	45	9	xn	xn	NUM
ma-207	45	10	)	)	PUNCT
ma-207	45	11	+	+	CCONJ
ma-207	45	12	g(xn+1	g(xn+1	NOUN
ma-207	45	13	)	)	PUNCT
ma-207	45	14	.	.	PUNCT
ma-207	46	1	modified	modify	VERB
ma-207	46	2	secant	secant	ADJ
ma-207	46	3	method	method	NOUN
ma-207	46	4	[	[	X
ma-207	46	5	4,5	4,5	NUM
ma-207	46	6	]	]	PUNCT
ma-207	46	7	:	:	PUNCT
ma-207	46	8	take	take	VERB
ma-207	46	9	l(xn	l(xn	NOUN
ma-207	46	10	)	)	PUNCT
ma-207	46	11	=	=	PUNCT
ma-207	47	1	[	[	X
ma-207	47	2	x−1	x−1	PROPN
ma-207	47	3	,	,	PUNCT
ma-207	47	4	x0;f	x0;f	PROPN
ma-207	47	5	]	]	X
ma-207	47	6	,	,	PUNCT
ma-207	47	7	x−1	x−1	PROPN
ma-207	47	8	,	,	PUNCT
ma-207	47	9	x0	x0	PROPN
ma-207	47	10	∈	∈	PROPN
ma-207	47	11	b−1	b−1	PROPN
ma-207	47	12	,	,	PUNCT
ma-207	47	13	n	n	NOUN
ma-207	47	14	=	=	SYM
ma-207	47	15	0	0	NUM
ma-207	47	16	,	,	PUNCT
ma-207	47	17	1	1	NUM
ma-207	47	18	,	,	PUNCT
ma-207	47	19	2	2	NUM
ma-207	47	20	,	,	PUNCT
ma-207	47	21	.	.	PUNCT
ma-207	47	22	.	.	PUNCT
ma-207	47	23	.	.	PUNCT
ma-207	48	1	to	to	PART
ma-207	48	2	obtain	obtain	VERB
ma-207	48	3	f	f	PROPN
ma-207	48	4	(	(	PUNCT
ma-207	48	5	xn	xn	PROPN
ma-207	48	6	)	)	PUNCT
ma-207	49	1	+	+	CCONJ
ma-207	50	1	[	[	X
ma-207	50	2	x−1	x−1	PROPN
ma-207	50	3	,	,	PUNCT
ma-207	50	4	x0;f	x0;f	PROPN
ma-207	50	5	]	]	X
ma-207	50	6	(	(	PUNCT
ma-207	50	7	xn+1	xn+1	NUM
ma-207	50	8	−	−	NOUN
ma-207	50	9	xn	xn	NUM
ma-207	50	10	)	)	PUNCT
ma-207	50	11	+	+	CCONJ
ma-207	50	12	g(xn+1	g(xn+1	NOUN
ma-207	50	13	)	)	PUNCT
ma-207	50	14	.	.	PUNCT
ma-207	51	1	kurchatov	kurchatov	PROPN
ma-207	51	2	method	method	PROPN
ma-207	52	1	[	[	X
ma-207	52	2	29,30	29,30	NUM
ma-207	52	3	]	]	PUNCT
ma-207	52	4	:	:	PUNCT
ma-207	52	5	set	set	VERB
ma-207	52	6	l(xn	l(xn	PROPN
ma-207	52	7	)	)	PUNCT
ma-207	52	8	=	=	PUNCT
ma-207	53	1	[	[	X
ma-207	53	2	2xn	2xn	ADJ
ma-207	53	3	−	−	X
ma-207	53	4	xn−1	xn−1	PROPN
ma-207	53	5	,	,	PUNCT
ma-207	53	6	xn−1;f	xn−1;f	PROPN
ma-207	53	7	]	]	PUNCT
ma-207	53	8	to	to	PART
ma-207	53	9	obtain	obtain	VERB
ma-207	53	10	f	f	PROPN
ma-207	53	11	(	(	PUNCT
ma-207	53	12	xn	xn	PROPN
ma-207	53	13	)	)	PUNCT
ma-207	53	14	+	+	CCONJ
ma-207	54	1	[	[	X
ma-207	54	2	2xn	2xn	ADJ
ma-207	54	3	−	−	NOUN
ma-207	54	4	xn−1	xn−1	PROPN
ma-207	54	5	,	,	PUNCT
ma-207	54	6	xn−1;f	xn−1;f	PROPN
ma-207	54	7	]	]	X
ma-207	54	8	(	(	PUNCT
ma-207	54	9	xn+1	xn+1	NUM
ma-207	54	10	−	−	NOUN
ma-207	54	11	xn	xn	NUM
ma-207	54	12	)	)	PUNCT
ma-207	54	13	+	+	CCONJ
ma-207	54	14	g(xn+1	g(xn+1	NOUN
ma-207	54	15	)	)	PUNCT
ma-207	54	16	.	.	PUNCT
ma-207	55	1	modified	modify	VERB
ma-207	55	2	kurchatov	kurchatov	ADJ
ma-207	55	3	method	method	NOUN
ma-207	56	1	[	[	X
ma-207	56	2	29,30	29,30	NUM
ma-207	56	3	]	]	PUNCT
ma-207	56	4	:	:	PUNCT
ma-207	56	5	let	let	VERB
ma-207	56	6	l(x	l(x	PROPN
ma-207	56	7	)	)	PUNCT
ma-207	56	8	=	=	PUNCT
ma-207	57	1	[	[	X
ma-207	57	2	2x0	2x0	NUM
ma-207	57	3	−	−	PROPN
ma-207	57	4	x−1	x−1	PROPN
ma-207	57	5	,	,	PUNCT
ma-207	57	6	x−1;f	x−1;f	PROPN
ma-207	57	7	]	]	PUNCT
ma-207	57	8	to	to	PART
ma-207	57	9	get	get	VERB
ma-207	57	10	f	f	PROPN
ma-207	57	11	(	(	PUNCT
ma-207	57	12	xn	xn	PROPN
ma-207	57	13	)	)	PUNCT
ma-207	58	1	+	+	CCONJ
ma-207	59	1	[	[	X
ma-207	59	2	2x0	2x0	NUM
ma-207	59	3	−	−	PROPN
ma-207	59	4	x−1	x−1	PROPN
ma-207	59	5	,	,	PUNCT
ma-207	59	6	x−1;f	x−1;f	PROPN
ma-207	59	7	]	]	PUNCT
ma-207	59	8	(	(	PUNCT
ma-207	59	9	xn+1	xn+1	NUM
ma-207	59	10	−	−	NOUN
ma-207	59	11	xn	xn	NUM
ma-207	59	12	)	)	PUNCT
ma-207	59	13	+	+	CCONJ
ma-207	59	14	g(xn+1	g(xn+1	NOUN
ma-207	59	15	)	)	PUNCT
ma-207	59	16	.	.	PUNCT
ma-207	60	1	https://doi.org/10.28924/ada/ma.4.3	https://doi.org/10.28924/ada/ma.4.3	PROPN
ma-207	60	2	eur	eur	PROPN
ma-207	60	3	.	.	PUNCT
ma-207	61	1	j.	j.	PROPN
ma-207	61	2	math	math	PROPN
ma-207	61	3	.	.	PUNCT
ma-207	62	1	anal	anal	PROPN
ma-207	62	2	.	.	PUNCT
ma-207	63	1	10.28924	10.28924	NUM
ma-207	63	2	/	/	SYM
ma-207	63	3	ada	ada	PROPN
ma-207	63	4	/	/	SYM
ma-207	63	5	ma.4.3	ma.4.3	PROPN
ma-207	63	6	3	3	NUM
ma-207	63	7	picard	picard	NOUN
ma-207	63	8	method	method	NOUN
ma-207	63	9	[	[	X
ma-207	63	10	20	20	NUM
ma-207	63	11	]	]	PUNCT
ma-207	63	12	:	:	PUNCT
ma-207	63	13	pick	pick	VERB
ma-207	63	14	l(x	l(x	PROPN
ma-207	63	15	)	)	PUNCT
ma-207	64	1	=	=	PUNCT
ma-207	64	2	i	i	PROPN
ma-207	64	3	,	,	PUNCT
ma-207	64	4	x	x	PROPN
ma-207	64	5	∈	∈	NOUN
ma-207	64	6	b1	b1	NOUN
ma-207	64	7	for	for	ADP
ma-207	64	8	b1	b1	NOUN
ma-207	64	9	=	=	SYM
ma-207	64	10	b2	b2	PROPN
ma-207	64	11	to	to	PART
ma-207	64	12	obtain	obtain	VERB
ma-207	64	13	f	f	PROPN
ma-207	64	14	(	(	PUNCT
ma-207	64	15	xn	xn	PROPN
ma-207	64	16	)	)	PUNCT
ma-207	65	1	+	+	CCONJ
ma-207	65	2	xn+1	xn+1	NUM
ma-207	65	3	−	−	NOUN
ma-207	65	4	xn	xn	PUNCT
ma-207	66	1	+	+	CCONJ
ma-207	66	2	g(xn+1	g(xn+1	NOUN
ma-207	66	3	)	)	PUNCT
ma-207	66	4	,	,	PUNCT
ma-207	66	5	n	n	NOUN
ma-207	66	6	=	=	SYM
ma-207	66	7	0	0	NUM
ma-207	66	8	,	,	PUNCT
ma-207	66	9	1	1	NUM
ma-207	66	10	,	,	PUNCT
ma-207	66	11	2	2	NUM
ma-207	66	12	,	,	PUNCT
ma-207	66	13	.	.	PUNCT
ma-207	66	14	.	.	PUNCT
ma-207	66	15	.	.	PUNCT
ma-207	67	1	.	.	PUNCT
ma-207	68	1	steffensen	steffensen	PROPN
ma-207	68	2	’s	’s	PART
ma-207	68	3	method	method	NOUN
ma-207	68	4	[	[	X
ma-207	68	5	4,5	4,5	NUM
ma-207	68	6	]	]	PUNCT
ma-207	68	7	:	:	PUNCT
ma-207	68	8	define	define	VERB
ma-207	68	9	l(x	l(x	PROPN
ma-207	68	10	)	)	PUNCT
ma-207	68	11	=	=	PUNCT
ma-207	69	1	[	[	X
ma-207	69	2	x	x	X
ma-207	69	3	+	+	NUM
ma-207	69	4	f	f	X
ma-207	69	5	(	(	PUNCT
ma-207	69	6	x	x	NOUN
ma-207	69	7	)	)	PUNCT
ma-207	69	8	,	,	PUNCT
ma-207	69	9	x	x	X
ma-207	69	10	−	−	PROPN
ma-207	69	11	f	f	X
ma-207	69	12	(	(	PUNCT
ma-207	69	13	x);f	x);f	INTJ
ma-207	69	14	]	]	X
ma-207	69	15	for	for	ADP
ma-207	69	16	b1	b1	NOUN
ma-207	69	17	=	=	SYM
ma-207	69	18	b2	b2	PROPN
ma-207	69	19	to	to	PART
ma-207	69	20	get	get	VERB
ma-207	69	21	f	f	PROPN
ma-207	69	22	(	(	PUNCT
ma-207	69	23	xn	xn	PROPN
ma-207	69	24	)	)	PUNCT
ma-207	69	25	+	+	CCONJ
ma-207	70	1	[	[	X
ma-207	70	2	xn	xn	X
ma-207	70	3	+	+	NUM
ma-207	70	4	f	f	X
ma-207	70	5	(	(	PUNCT
ma-207	70	6	xn	xn	PROPN
ma-207	70	7	)	)	PUNCT
ma-207	70	8	,	,	PUNCT
ma-207	70	9	xn	xn	PROPN
ma-207	71	1	−	−	PROPN
ma-207	71	2	f	f	X
ma-207	71	3	(	(	PUNCT
ma-207	71	4	xn);f	xn);f	PROPN
ma-207	71	5	]	]	PUNCT
ma-207	71	6	(	(	PUNCT
ma-207	71	7	xn+1	xn+1	NUM
ma-207	71	8	−	−	NOUN
ma-207	71	9	xn	xn	NUM
ma-207	71	10	)	)	PUNCT
ma-207	71	11	+	+	CCONJ
ma-207	71	12	g(xn+1	g(xn+1	NOUN
ma-207	71	13	)	)	PUNCT
ma-207	71	14	,	,	PUNCT
ma-207	71	15	n	n	NOUN
ma-207	71	16	=	=	SYM
ma-207	71	17	0	0	NUM
ma-207	71	18	,	,	PUNCT
ma-207	71	19	1	1	NUM
ma-207	71	20	,	,	PUNCT
ma-207	71	21	2	2	NUM
ma-207	71	22	,	,	PUNCT
ma-207	71	23	.	.	PUNCT
ma-207	71	24	.	.	PUNCT
ma-207	71	25	.	.	PUNCT
ma-207	71	26	.	.	PUNCT
ma-207	72	1	stirling	stirling	NOUN
ma-207	72	2	’s	’s	PART
ma-207	72	3	method	method	NOUN
ma-207	72	4	[	[	X
ma-207	72	5	20,31	20,31	NUM
ma-207	72	6	]	]	PUNCT
ma-207	72	7	:	:	PUNCT
ma-207	72	8	define	define	VERB
ma-207	72	9	l(x	l(x	PROPN
ma-207	72	10	)	)	PUNCT
ma-207	73	1	=	=	SYM
ma-207	74	1	i	i	PRON
ma-207	74	2	−	−	VERB
ma-207	74	3	f	f	PROPN
ma-207	74	4	′(x	′(x	PROPN
ma-207	74	5	)	)	PUNCT
ma-207	74	6	,	,	PUNCT
ma-207	74	7	x	x	PUNCT
ma-207	74	8	∈	∈	NOUN
ma-207	74	9	b1	b1	NOUN
ma-207	74	10	to	to	PART
ma-207	74	11	obtain	obtain	VERB
ma-207	74	12	f	f	PROPN
ma-207	74	13	(	(	PUNCT
ma-207	74	14	xn	xn	PROPN
ma-207	74	15	)	)	PUNCT
ma-207	75	1	+	+	CCONJ
ma-207	75	2	(	(	PUNCT
ma-207	75	3	i	i	PRON
ma-207	75	4	−	−	PROPN
ma-207	75	5	f	f	PROPN
ma-207	75	6	′(xn))(xn+1	′(xn))(xn+1	PROPN
ma-207	75	7	−	−	PROPN
ma-207	75	8	xn	xn	X
ma-207	75	9	)	)	PUNCT
ma-207	76	1	+	+	CCONJ
ma-207	76	2	g(xn+1	g(xn+1	NOUN
ma-207	76	3	)	)	PUNCT
ma-207	76	4	,	,	PUNCT
ma-207	76	5	n	n	NOUN
ma-207	76	6	=	=	SYM
ma-207	76	7	0	0	NUM
ma-207	76	8	,	,	PUNCT
ma-207	76	9	1	1	NUM
ma-207	76	10	,	,	PUNCT
ma-207	76	11	2	2	NUM
ma-207	76	12	,	,	PUNCT
ma-207	76	13	.	.	PUNCT
ma-207	76	14	.	.	PUNCT
ma-207	76	15	.	.	PUNCT
ma-207	77	1	.	.	PUNCT
ma-207	78	1	traub	traub	PROPN
ma-207	78	2	and	and	CCONJ
ma-207	78	3	other	other	ADJ
ma-207	78	4	multi	multi	ADJ
ma-207	78	5	-	-	NOUN
ma-207	78	6	point	point	NOUN
ma-207	78	7	and	and	CCONJ
ma-207	78	8	multi	multi	ADJ
ma-207	78	9	-	-	ADJ
ma-207	78	10	step	step	ADJ
ma-207	78	11	methods	method	NOUN
ma-207	78	12	[	[	X
ma-207	78	13	4,5,17,31,32	4,5,17,31,32	VERB
ma-207	78	14	]	]	PUNCT
ma-207	78	15	:	:	PUNCT
ma-207	78	16	therefore	therefore	ADV
ma-207	78	17	,	,	PUNCT
ma-207	78	18	it	it	PRON
ma-207	78	19	is	be	AUX
ma-207	78	20	importantto	importantto	ADJ
ma-207	78	21	develop	develop	VERB
ma-207	78	22	unifying	unifying	ADJ
ma-207	78	23	conditions	condition	NOUN
ma-207	78	24	for	for	ADP
ma-207	78	25	the	the	DET
ma-207	78	26	convergence	convergence	NOUN
ma-207	78	27	of	of	ADP
ma-207	78	28	(	(	PUNCT
ma-207	78	29	1.2	1.2	NUM
ma-207	78	30	)	)	PUNCT
ma-207	78	31	.	.	PUNCT
ma-207	79	1	there	there	PRON
ma-207	79	2	are	be	VERB
ma-207	79	3	two	two	NUM
ma-207	79	4	popular	popular	ADJ
ma-207	79	5	convergenceapproaches	convergenceapproache	NOUN
ma-207	79	6	in	in	ADP
ma-207	79	7	the	the	DET
ma-207	79	8	literature	literature	NOUN
ma-207	79	9	.	.	PUNCT
ma-207	80	1	we	we	PRON
ma-207	80	2	develop	develop	VERB
ma-207	80	3	,	,	PUNCT
ma-207	80	4	the	the	DET
ma-207	80	5	semi	semi	ADJ
ma-207	80	6	-	-	ADJ
ma-207	80	7	local	local	ADJ
ma-207	80	8	analysis	analysis	NOUN
ma-207	80	9	of	of	ADP
ma-207	80	10	convergence	convergence	NOUN
ma-207	80	11	.	.	PUNCT
ma-207	81	1	in	in	ADP
ma-207	81	2	the	the	DET
ma-207	81	3	localcase	localcase	ADJ
ma-207	81	4	information	information	NOUN
ma-207	81	5	is	be	AUX
ma-207	81	6	used	use	VERB
ma-207	81	7	to	to	PART
ma-207	81	8	produce	produce	VERB
ma-207	81	9	usually	usually	ADV
ma-207	81	10	a	a	DET
ma-207	81	11	ball	ball	NOUN
ma-207	81	12	centered	center	VERB
ma-207	81	13	at	at	ADP
ma-207	81	14	x∗	x∗	PROPN
ma-207	81	15	,	,	PUNCT
ma-207	81	16	so	so	SCONJ
ma-207	81	17	that	that	SCONJ
ma-207	81	18	if	if	SCONJ
ma-207	81	19	one	one	PRON
ma-207	81	20	picks	pick	VERB
ma-207	81	21	a	a	DET
ma-207	81	22	pointinside	pointinside	NOUN
ma-207	81	23	of	of	ADP
ma-207	81	24	it	it	PRON
ma-207	81	25	the	the	DET
ma-207	81	26	convergence	convergence	NOUN
ma-207	81	27	of	of	ADP
ma-207	81	28	the	the	DET
ma-207	81	29	iterative	iterative	NOUN
ma-207	81	30	method	method	NOUN
ma-207	81	31	is	be	AUX
ma-207	81	32	assured	assure	VERB
ma-207	81	33	.	.	PUNCT
ma-207	82	1	note	note	VERB
ma-207	82	2	that	that	SCONJ
ma-207	82	3	,	,	PUNCT
ma-207	82	4	in	in	ADP
ma-207	82	5	the	the	DET
ma-207	82	6	semi	semi	ADJ
ma-207	82	7	-	-	ADJ
ma-207	82	8	localcase	localcase	ADJ
ma-207	82	9	the	the	DET
ma-207	82	10	convergence	convergence	NOUN
ma-207	82	11	ball	ball	NOUN
ma-207	82	12	is	be	AUX
ma-207	82	13	centered	center	VERB
ma-207	82	14	at	at	ADP
ma-207	82	15	the	the	DET
ma-207	82	16	starting	starting	NOUN
ma-207	82	17	point	point	NOUN
ma-207	82	18	x0	x0	PROPN
ma-207	82	19	.	.	PUNCT
ma-207	83	1	the	the	DET
ma-207	83	2	convergence	convergence	NOUN
ma-207	83	3	conditions	condition	NOUN
ma-207	83	4	usuallyinvolve	usuallyinvolve	VERB
ma-207	83	5	lipschitz	lipschitz	VERB
ma-207	83	6	[	[	X
ma-207	83	7	4	4	NUM
ma-207	83	8	,	,	PUNCT
ma-207	83	9	5	5	NUM
ma-207	83	10	]	]	PUNCT
ma-207	83	11	and	and	CCONJ
ma-207	83	12	hölder	hölder	NOUN
ma-207	83	13	-	-	PUNCT
ma-207	83	14	type	type	NOUN
ma-207	83	15	conditions	condition	NOUN
ma-207	83	16	[	[	X
ma-207	83	17	20	20	NUM
ma-207	83	18	]	]	PUNCT
ma-207	83	19	.	.	PUNCT
ma-207	84	1	the	the	DET
ma-207	84	2	new	new	ADJ
ma-207	84	3	convergence	convergence	NOUN
ma-207	84	4	analysis	analysis	NOUN
ma-207	84	5	in	in	ADP
ma-207	84	6	bothcases	bothcase	NOUN
ma-207	84	7	involves	involve	VERB
ma-207	84	8	generalized	generalized	ADJ
ma-207	84	9	continuity	continuity	NOUN
ma-207	84	10	conditions	condition	NOUN
ma-207	84	11	,	,	PUNCT
ma-207	84	12	majorant	majorant	NOUN
ma-207	84	13	functions	function	NOUN
ma-207	84	14	,	,	PUNCT
ma-207	84	15	majorizing	majorize	VERB
ma-207	84	16	sequences	sequence	NOUN
ma-207	84	17	(	(	PUNCT
ma-207	84	18	in	in	ADP
ma-207	84	19	thesemi	thesemi	NOUN
ma-207	84	20	-	-	ADJ
ma-207	84	21	local	local	ADJ
ma-207	84	22	case	case	NOUN
ma-207	84	23	)	)	PUNCT
ma-207	84	24	in	in	ADP
ma-207	84	25	combination	combination	NOUN
ma-207	84	26	under	under	ADP
ma-207	84	27	the	the	DET
ma-207	84	28	aubin	aubin	PROPN
ma-207	84	29	property	property	NOUN
ma-207	84	30	of	of	ADP
ma-207	84	31	the	the	DET
ma-207	84	32	set	set	NOUN
ma-207	84	33	valued	value	VERB
ma-207	84	34	operator	operator	NOUN
ma-207	84	35	on	on	ADP
ma-207	84	36	the	the	DET
ma-207	84	37	methodand	methodand	NOUN
ma-207	84	38	the	the	DET
ma-207	84	39	celebrated	celebrated	ADJ
ma-207	84	40	contraction	contraction	NOUN
ma-207	84	41	mapping	mapping	NOUN
ma-207	84	42	principle	principle	NOUN
ma-207	84	43	[	[	X
ma-207	84	44	15	15	NUM
ma-207	84	45	]	]	PUNCT
ma-207	84	46	.	.	PUNCT
ma-207	85	1	upper	upper	ADJ
ma-207	85	2	error	error	NOUN
ma-207	85	3	estimates	estimate	NOUN
ma-207	85	4	on	on	ADP
ma-207	85	5	‖x∗	‖x∗	PUNCT
ma-207	85	6	−	−	PROPN
ma-207	86	1	xn‖	xn‖	PROPN
ma-207	86	2	for	for	ADP
ma-207	86	3	thesolution	thesolution	NOUN
ma-207	86	4	are	be	AUX
ma-207	86	5	developed	develop	VERB
ma-207	86	6	which	which	PRON
ma-207	86	7	are	be	AUX
ma-207	86	8	computable.the	computable.the	DET
ma-207	86	9	rest	rest	NOUN
ma-207	86	10	of	of	ADP
ma-207	86	11	the	the	DET
ma-207	86	12	article	article	NOUN
ma-207	86	13	contains	contain	VERB
ma-207	86	14	:	:	PUNCT
ma-207	86	15	the	the	DET
ma-207	86	16	mathematical	mathematical	ADJ
ma-207	86	17	background	background	NOUN
ma-207	86	18	necessary	necessary	ADJ
ma-207	86	19	to	to	PART
ma-207	86	20	make	make	VERB
ma-207	86	21	this	this	DET
ma-207	86	22	article	article	NOUN
ma-207	86	23	asself	asself	PROPN
ma-207	86	24	contained	contain	VERB
ma-207	86	25	as	as	ADP
ma-207	86	26	possible	possible	ADJ
ma-207	86	27	appears	appear	VERB
ma-207	86	28	in	in	ADP
ma-207	86	29	section	section	NOUN
ma-207	86	30	2	2	NUM
ma-207	86	31	;	;	PUNCT
ma-207	86	32	semi	semi	ADJ
ma-207	86	33	-	-	ADJ
ma-207	86	34	local	local	ADJ
ma-207	86	35	convergence	convergence	NOUN
ma-207	86	36	results	result	NOUN
ma-207	86	37	appear	appear	VERB
ma-207	86	38	is	be	AUX
ma-207	86	39	section3	section3	PROPN
ma-207	86	40	.	.	PUNCT
ma-207	87	1	the	the	DET
ma-207	87	2	article	article	NOUN
ma-207	87	3	ends	end	VERB
ma-207	87	4	with	with	ADP
ma-207	87	5	concluding	conclude	VERB
ma-207	87	6	remarks	remark	NOUN
ma-207	87	7	in	in	ADP
ma-207	87	8	section	section	NOUN
ma-207	87	9	4	4	NUM
ma-207	87	10	.	.	NOUN
ma-207	87	11	2	2	NUM
ma-207	87	12	.	.	X
ma-207	87	13	mathematical	mathematical	PROPN
ma-207	87	14	bachground	bachground	PROPN
ma-207	87	15	certain	certain	ADJ
ma-207	87	16	standard	standard	ADJ
ma-207	87	17	concepts	concept	NOUN
ma-207	87	18	are	be	AUX
ma-207	87	19	restated	restate	VERB
ma-207	87	20	in	in	ADP
ma-207	87	21	order	order	NOUN
ma-207	87	22	to	to	PART
ma-207	87	23	make	make	VERB
ma-207	87	24	the	the	DET
ma-207	87	25	article	article	NOUN
ma-207	87	26	as	as	SCONJ
ma-207	87	27	self	self	NOUN
ma-207	87	28	-	-	PUNCT
ma-207	87	29	contained	contain	VERB
ma-207	87	30	as	as	SCONJ
ma-207	87	31	possible.more	possible.more	DET
ma-207	87	32	detailed	detailed	ADJ
ma-207	87	33	information	information	NOUN
ma-207	87	34	can	can	AUX
ma-207	87	35	be	be	AUX
ma-207	87	36	found	find	VERB
ma-207	87	37	in	in	ADP
ma-207	87	38	[	[	PUNCT
ma-207	87	39	15].the	15].the	DET
ma-207	87	40	graph	graph	NOUN
ma-207	87	41	of	of	ADP
ma-207	87	42	a	a	DET
ma-207	87	43	set	set	NOUN
ma-207	87	44	-	-	PUNCT
ma-207	87	45	valued	value	VERB
ma-207	87	46	operator	operator	NOUN
ma-207	87	47	g	g	NOUN
ma-207	87	48	:	:	PUNCT
ma-207	87	49	b1	b1	PROPN
ma-207	87	50	⇒	⇒	PROPN
ma-207	87	51	b2	b2	PROPN
ma-207	87	52	is	be	AUX
ma-207	87	53	gpg	gpg	X
ma-207	87	54	=	=	X
ma-207	87	55	{	{	PUNCT
ma-207	87	56	(	(	PUNCT
ma-207	87	57	v1	v1	NOUN
ma-207	87	58	,	,	PUNCT
ma-207	87	59	v2	v2	NOUN
ma-207	87	60	)	)	PUNCT
ma-207	87	61	∈	∈	PROPN
ma-207	87	62	b1	b1	NOUN
ma-207	87	63	×	×	PROPN
ma-207	87	64	b2	b2	NOUN
ma-207	87	65	:	:	PUNCT
ma-207	87	66	v2	v2	PROPN
ma-207	87	67	∈	∈	PROPN
ma-207	87	68	g(v1	g(v1	NOUN
ma-207	87	69	)	)	PUNCT
ma-207	87	70	}	}	PUNCT
ma-207	87	71	the	the	DET
ma-207	87	72	domain	domain	NOUN
ma-207	87	73	dom(g	dom(g	ADV
ma-207	87	74	)	)	PUNCT
ma-207	87	75	=	=	PRON
ma-207	87	76	{	{	PUNCT
ma-207	87	77	v	v	NUM
ma-207	87	78	∈	∈	PROPN
ma-207	87	79	b1	b1	NOUN
ma-207	87	80	:	:	PUNCT
ma-207	87	81	g(v	g(v	PROPN
ma-207	87	82	)	)	PUNCT
ma-207	87	83	6=	6=	ADP
ma-207	87	84	∅	∅	NOUN
ma-207	87	85	}	}	PUNCT
ma-207	87	86	;	;	PUNCT
ma-207	87	87	the	the	DET
ma-207	87	88	rge(g	rge(g	NOUN
ma-207	87	89	)	)	PUNCT
ma-207	87	90	=	=	PRON
ma-207	87	91	{	{	PUNCT
ma-207	87	92	v2	v2	PROPN
ma-207	87	93	∈	∈	PROPN
ma-207	87	94	b2	b2	NOUN
ma-207	87	95	:	:	PUNCT
ma-207	87	96	for	for	ADP
ma-207	87	97	some	some	DET
ma-207	87	98	v1	v1	NOUN
ma-207	87	99	∈	∈	PROPN
ma-207	87	100	b1	b1	NOUN
ma-207	87	101	,	,	PUNCT
ma-207	87	102	v2	v2	PROPN
ma-207	87	103	∈	∈	PROPN
ma-207	87	104	g(v1)}.moreover	g(v1)}.moreover	NOUN
ma-207	87	105	,	,	PUNCT
ma-207	87	106	the	the	DET
ma-207	87	107	inverse	inverse	NOUN
ma-207	87	108	g−1	g−1	PROPN
ma-207	87	109	:	:	PUNCT
ma-207	87	110	b2	b2	NOUN
ma-207	87	111	⇒	⇒	NOUN
ma-207	87	112	b1	b1	PROPN
ma-207	87	113	is	be	AUX
ma-207	87	114	g−1(v2	g−1(v2	NOUN
ma-207	87	115	)	)	PUNCT
ma-207	87	116	=	=	SYM
ma-207	87	117	{	{	PUNCT
ma-207	87	118	v1	v1	PROPN
ma-207	87	119	∈	∈	PROPN
ma-207	87	120	b	b	NOUN
ma-207	87	121	−	−	NOUN
ma-207	87	122	1	1	NUM
ma-207	87	123	:	:	PUNCT
ma-207	87	124	v2	v2	PROPN
ma-207	87	125	∈	∈	PROPN
ma-207	87	126	g(v1	g(v1	NOUN
ma-207	87	127	)	)	PUNCT
ma-207	87	128	}	}	PUNCT
ma-207	87	129	.	.	PUNCT
ma-207	88	1	furthermore	furthermore	ADV
ma-207	88	2	,	,	PUNCT
ma-207	88	3	for	for	ADP
ma-207	88	4	sets	set	NOUN
ma-207	88	5	c1	c1	PROPN
ma-207	88	6	and	and	CCONJ
ma-207	88	7	c2	c2	PROPN
ma-207	88	8	in	in	ADP
ma-207	88	9	b1	b1	PROPN
ma-207	88	10	,	,	PUNCT
ma-207	88	11	define	define	VERB
ma-207	88	12	d(v	d(v	PROPN
ma-207	88	13	,	,	PUNCT
ma-207	88	14	c1	c1	PROPN
ma-207	88	15	)	)	PUNCT
ma-207	89	1	=	=	X
ma-207	89	2	inf	inf	PROPN
ma-207	89	3	v1∈c1	v1∈c1	VERB
ma-207	89	4	d(v	d(v	PROPN
ma-207	89	5	,	,	PUNCT
ma-207	89	6	v1	v1	NOUN
ma-207	89	7	)	)	PUNCT
ma-207	89	8	and	and	CCONJ
ma-207	89	9	e(c1	e(c1	NOUN
ma-207	89	10	,	,	PUNCT
ma-207	89	11	c2	c2	PROPN
ma-207	89	12	)	)	PUNCT
ma-207	89	13	=	=	PUNCT
ma-207	90	1	sup	sup	NOUN
ma-207	90	2	v1∈c1	v1∈c1	NUM
ma-207	90	3	d(v	d(v	PROPN
ma-207	90	4	,	,	PUNCT
ma-207	90	5	c2	c2	PROPN
ma-207	90	6	)	)	PUNCT
ma-207	90	7	,	,	PUNCT
ma-207	90	8	https://doi.org/10.28924/ada/ma.4.3	https://doi.org/10.28924/ada/ma.4.3	PROPN
ma-207	90	9	eur	eur	PROPN
ma-207	90	10	.	.	PUNCT
ma-207	91	1	j.	j.	PROPN
ma-207	91	2	math	math	PROPN
ma-207	91	3	.	.	PUNCT
ma-207	92	1	anal	anal	PROPN
ma-207	92	2	.	.	PUNCT
ma-207	93	1	10.28924	10.28924	NUM
ma-207	93	2	/	/	SYM
ma-207	93	3	ada	ada	PROPN
ma-207	93	4	/	/	SYM
ma-207	93	5	ma.4.3	ma.4.3	PROPN
ma-207	93	6	4where	4where	PROPN
ma-207	93	7	d	d	PROPN
ma-207	93	8	,	,	PUNCT
ma-207	93	9	e	e	NOUN
ma-207	93	10	are	be	AUX
ma-207	93	11	standard	standard	ADJ
ma-207	93	12	symbols	symbol	NOUN
ma-207	93	13	for	for	ADP
ma-207	93	14	the	the	DET
ma-207	93	15	distance	distance	NOUN
ma-207	93	16	from	from	ADP
ma-207	93	17	v	v	NUM
ma-207	93	18	to	to	ADP
ma-207	93	19	c2	c2	PROPN
ma-207	93	20	and	and	CCONJ
ma-207	93	21	the	the	DET
ma-207	93	22	excess	excess	NOUN
ma-207	93	23	of	of	ADP
ma-207	93	24	c1	c1	PROPN
ma-207	93	25	to	to	ADP
ma-207	93	26	c2	c2	PROPN
ma-207	93	27	.	.	PUNCT
ma-207	94	1	recallthat	recallthat	DET
ma-207	94	2	e(∅	e(∅	ADV
ma-207	94	3	,	,	PUNCT
ma-207	94	4	∅	∅	NOUN
ma-207	94	5	)	)	PUNCT
ma-207	94	6	=	=	PUNCT
ma-207	95	1	+	+	NOUN
ma-207	95	2	∞	∞	PROPN
ma-207	95	3	,	,	PUNCT
ma-207	95	4	d(v	d(v	PROPN
ma-207	95	5	,	,	PUNCT
ma-207	95	6	c2	c2	PROPN
ma-207	95	7	)	)	PUNCT
ma-207	95	8	=	=	PUNCT
ma-207	96	1	+	+	NUM
ma-207	96	2	∞	∞	PROPN
ma-207	96	3	,	,	PUNCT
ma-207	96	4	if	if	SCONJ
ma-207	96	5	c2	c2	PROPN
ma-207	96	6	=	=	PUNCT
ma-207	96	7	∅	∅	NOUN
ma-207	96	8	and	and	CCONJ
ma-207	96	9	e(∅	e(∅	ADV
ma-207	96	10	,	,	PUNCT
ma-207	96	11	c2	c2	PROPN
ma-207	96	12	)	)	PUNCT
ma-207	96	13	=	=	SYM
ma-207	97	1	0	0	NUM
ma-207	97	2	,	,	PUNCT
ma-207	97	3	if	if	SCONJ
ma-207	97	4	c2	c2	PROPN
ma-207	97	5	6=	6=	PUNCT
ma-207	97	6	∅	∅	NOUN
ma-207	97	7	(	(	PUNCT
ma-207	97	8	by	by	ADP
ma-207	97	9	convention	convention	NOUN
ma-207	97	10	)	)	PUNCT
ma-207	97	11	,	,	PUNCT
ma-207	97	12	where	where	SCONJ
ma-207	97	13	∅	∅	NOUN
ma-207	97	14	is	be	AUX
ma-207	97	15	the	the	DET
ma-207	97	16	symbol	symbol	NOUN
ma-207	97	17	for	for	ADP
ma-207	97	18	the	the	DET
ma-207	97	19	empty	empty	ADJ
ma-207	97	20	set.next	set.next	NOUN
ma-207	97	21	,	,	PUNCT
ma-207	97	22	some	some	DET
ma-207	97	23	more	more	ADJ
ma-207	97	24	definitions	definition	NOUN
ma-207	97	25	and	and	CCONJ
ma-207	97	26	standard	standard	ADJ
ma-207	97	27	results	result	NOUN
ma-207	97	28	are	be	AUX
ma-207	97	29	stated	state	VERB
ma-207	97	30	.	.	PUNCT
ma-207	98	1	definition	definition	NOUN
ma-207	98	2	2.1	2.1	NUM
ma-207	98	3	.	.	PUNCT
ma-207	99	1	the	the	DET
ma-207	99	2	inverse	inverse	NOUN
ma-207	99	3	operator	operator	NOUN
ma-207	99	4	g−1	g−1	PROPN
ma-207	99	5	of	of	ADP
ma-207	99	6	g	g	PROPN
ma-207	99	7	has	have	VERB
ma-207	99	8	the	the	DET
ma-207	99	9	aubin	aubin	PROPN
ma-207	99	10	property	property	NOUN
ma-207	99	11	for	for	ADP
ma-207	99	12	v1	v1	NOUN
ma-207	99	13	∈	∈	NOUN
ma-207	99	14	b1	b1	NOUN
ma-207	99	15	at	at	ADP
ma-207	99	16	v2	v2	PROPN
ma-207	99	17	∈	∈	PROPN
ma-207	99	18	b2	b2	NOUN
ma-207	99	19	of	of	ADP
ma-207	99	20	modulus	modulus	ADJ
ma-207	99	21	λ	λ	PROPN
ma-207	99	22	≥	≥	NOUN
ma-207	99	23	0	0	NUM
ma-207	99	24	,	,	PUNCT
ma-207	99	25	if	if	SCONJ
ma-207	99	26	when	when	SCONJ
ma-207	99	27	v1	v1	PROPN
ma-207	99	28	∈	∈	PROPN
ma-207	99	29	g−1(v2	g−1(v2	NOUN
ma-207	99	30	)	)	PUNCT
ma-207	99	31	,	,	PUNCT
ma-207	99	32	there	there	PRON
ma-207	99	33	exist	exist	VERB
ma-207	99	34	α	α	PROPN
ma-207	99	35	>	>	X
ma-207	99	36	0	0	PUNCT
ma-207	99	37	and	and	CCONJ
ma-207	99	38	β	β	X
ma-207	99	39	>	>	X
ma-207	99	40	0	0	PUNCT
ma-207	100	1	so	so	SCONJ
ma-207	100	2	that	that	SCONJ
ma-207	100	3	e(g−1(v4	e(g−1(v4	NUM
ma-207	100	4	)	)	PUNCT
ma-207	101	1	∩h[v1	∩h[v1	NUM
ma-207	101	2	,	,	PUNCT
ma-207	101	3	α	α	NOUN
ma-207	101	4	]	]	X
ma-207	101	5	,	,	PUNCT
ma-207	101	6	g−1(v3	g−1(v3	NOUN
ma-207	101	7	)	)	PUNCT
ma-207	101	8	)	)	PUNCT
ma-207	102	1	≤	≤	PUNCT
ma-207	103	1	λ‖v4	λ‖v4	PROPN
ma-207	104	1	−	−	PROPN
ma-207	104	2	v3‖	v3‖	PROPN
ma-207	104	3	for	for	ADP
ma-207	104	4	each	each	DET
ma-207	104	5	v3	v3	NOUN
ma-207	104	6	,	,	PUNCT
ma-207	104	7	v4	v4	NOUN
ma-207	104	8	∈	∈	PROPN
ma-207	104	9	h[v2	h[v2	NOUN
ma-207	104	10	,	,	PUNCT
ma-207	104	11	β	β	X
ma-207	104	12	]	]	X
ma-207	104	13	(	(	PUNCT
ma-207	104	14	2.1	2.1	NUM
ma-207	104	15	)	)	PUNCT
ma-207	104	16	and	and	CCONJ
ma-207	104	17	the	the	DET
ma-207	104	18	inverse	inverse	NOUN
ma-207	104	19	operator	operator	NOUN
ma-207	104	20	g−1	g−1	PROPN
ma-207	104	21	is	be	AUX
ma-207	104	22	locally	locally	ADV
ma-207	104	23	closed	close	VERB
ma-207	104	24	at	at	ADP
ma-207	104	25	the	the	DET
ma-207	104	26	pair	pair	NOUN
ma-207	104	27	(	(	PUNCT
ma-207	104	28	v2	v2	NOUN
ma-207	104	29	,	,	PUNCT
ma-207	104	30	v1	v1	NOUN
ma-207	104	31	)	)	PUNCT
ma-207	104	32	,	,	PUNCT
ma-207	104	33	where	where	SCONJ
ma-207	104	34	h(v	h(v	PROPN
ma-207	104	35	,	,	PUNCT
ma-207	104	36	α	α	NOUN
ma-207	104	37	)	)	PUNCT
ma-207	104	38	,	,	PUNCT
ma-207	104	39	h[v	h[v	PROPN
ma-207	104	40	,	,	PUNCT
ma-207	104	41	α	α	X
ma-207	104	42	]	]	X
ma-207	104	43	denote	denote	VERB
ma-207	104	44	open	open	ADJ
ma-207	104	45	and	and	CCONJ
ma-207	104	46	closed	closed	ADJ
ma-207	104	47	balls	ball	NOUN
ma-207	104	48	,	,	PUNCT
ma-207	104	49	respectively	respectively	ADV
ma-207	104	50	of	of	ADP
ma-207	104	51	center	center	NOUN
ma-207	104	52	v	v	NUM
ma-207	104	53	∈	∈	PROPN
ma-207	104	54	b1	b1	NOUN
ma-207	104	55	with	with	ADP
ma-207	104	56	radius	radius	NOUN
ma-207	104	57	α	α	PROPN
ma-207	104	58	>	>	X
ma-207	104	59	0	0	X
ma-207	104	60	.	.	PUNCT
ma-207	105	1	it	it	PRON
ma-207	105	2	is	be	AUX
ma-207	105	3	useful	useful	ADJ
ma-207	105	4	to	to	PART
ma-207	105	5	recall	recall	VERB
ma-207	105	6	that	that	SCONJ
ma-207	105	7	there	there	PRON
ma-207	105	8	is	be	VERB
ma-207	105	9	a	a	DET
ma-207	105	10	relationship	relationship	NOUN
ma-207	105	11	between	between	ADP
ma-207	105	12	the	the	DET
ma-207	105	13	aubin	aubin	PROPN
ma-207	105	14	property	property	NOUN
ma-207	105	15	and	and	CCONJ
ma-207	105	16	the	the	DET
ma-207	105	17	metricregularity	metricregularity	NOUN
ma-207	105	18	(	(	PUNCT
ma-207	105	19	see	see	VERB
ma-207	105	20	e.g.	e.g.	ADV
ma-207	105	21	[	[	X
ma-207	105	22	15	15	NUM
ma-207	105	23	,	,	PUNCT
ma-207	105	24	theorem	theorem	VERB
ma-207	105	25	3.7	3.7	NUM
ma-207	105	26	]	]	PUNCT
ma-207	105	27	)	)	PUNCT
ma-207	105	28	.	.	PUNCT
ma-207	106	1	in	in	ADP
ma-207	106	2	particular	particular	ADJ
ma-207	106	3	,	,	PUNCT
ma-207	106	4	g−1	g−1	PROPN
ma-207	106	5	:	:	PUNCT
ma-207	106	6	b2	b2	NOUN
ma-207	106	7	⇒	⇒	NOUN
ma-207	106	8	b1	b1	PROPN
ma-207	106	9	has	have	VERB
ma-207	106	10	the	the	DET
ma-207	106	11	aubin	aubin	PROPN
ma-207	106	12	property	property	NOUN
ma-207	106	13	at	at	ADP
ma-207	106	14	v1	v1	NOUN
ma-207	106	15	,	,	PUNCT
ma-207	106	16	v2	v2	PROPN
ma-207	106	17	)	)	PUNCT
ma-207	106	18	with	with	ADP
ma-207	106	19	modulus	modulus	NOUN
ma-207	106	20	λ	λ	PROPN
ma-207	106	21	>	>	X
ma-207	106	22	0	0	PUNCT
ma-207	107	1	if	if	SCONJ
ma-207	107	2	and	and	CCONJ
ma-207	107	3	only	only	ADV
ma-207	107	4	if	if	SCONJ
ma-207	107	5	g	g	NOUN
ma-207	107	6	:	:	PUNCT
ma-207	107	7	b1	b1	PROPN
ma-207	107	8	⇒	⇒	NOUN
ma-207	107	9	b2	b2	PROPN
ma-207	107	10	is	be	AUX
ma-207	107	11	metrically	metrically	ADV
ma-207	107	12	regular	regular	ADJ
ma-207	107	13	at	at	ADP
ma-207	107	14	(	(	PUNCT
ma-207	107	15	v1	v1	NOUN
ma-207	107	16	,	,	PUNCT
ma-207	107	17	v2	v2	PROPN
ma-207	107	18	)	)	PUNCT
ma-207	107	19	with	with	ADP
ma-207	107	20	the	the	DET
ma-207	107	21	sameconstant	sameconstant	PROPN
ma-207	107	22	λ	λ	PROPN
ma-207	107	23	.	.	PUNCT
ma-207	108	1	therefore	therefore	ADV
ma-207	108	2	,	,	PUNCT
ma-207	108	3	the	the	DET
ma-207	108	4	results	result	NOUN
ma-207	108	5	that	that	PRON
ma-207	108	6	follows	follow	VERB
ma-207	108	7	are	be	AUX
ma-207	108	8	given	give	VERB
ma-207	108	9	equivalently	equivalently	ADV
ma-207	108	10	in	in	ADP
ma-207	108	11	terms	term	NOUN
ma-207	108	12	of	of	ADP
ma-207	108	13	metric	metric	ADJ
ma-207	108	14	regularity.the	regularity.the	PRON
ma-207	108	15	celebrated	celebrate	VERB
ma-207	108	16	contraction	contraction	NOUN
ma-207	108	17	mapping	mapping	NOUN
ma-207	108	18	principle	principle	NOUN
ma-207	108	19	[	[	X
ma-207	108	20	15,21,22	15,21,22	X
ma-207	108	21	]	]	X
ma-207	108	22	plays	play	VERB
ma-207	108	23	a	a	DET
ma-207	108	24	vital	vital	ADJ
ma-207	108	25	role	role	NOUN
ma-207	108	26	in	in	ADP
ma-207	108	27	our	our	PRON
ma-207	108	28	investigations	investigation	NOUN
ma-207	108	29	.	.	PUNCT
ma-207	109	1	theorem	theorem	VERB
ma-207	109	2	2.2	2.2	NUM
ma-207	109	3	.	.	PUNCT
ma-207	110	1	let	let	VERB
ma-207	110	2	us	we	PRON
ma-207	110	3	consider	consider	VERB
ma-207	110	4	a	a	DET
ma-207	110	5	set	set	NOUN
ma-207	110	6	-	-	PUNCT
ma-207	110	7	valued	value	VERB
ma-207	110	8	operator	operator	NOUN
ma-207	110	9	ψ	ψ	NOUN
ma-207	110	10	:	:	PUNCT
ma-207	110	11	b1	b1	NOUN
ma-207	110	12	⇒	⇒	NOUN
ma-207	110	13	b2	b2	PROPN
ma-207	110	14	and	and	CCONJ
ma-207	110	15	v	v	ADP
ma-207	110	16	∈	∈	PROPN
ma-207	110	17	b1	b1	NOUN
ma-207	110	18	.	.	PUNCT
ma-207	111	1	assume	assume	VERB
ma-207	111	2	that	that	SCONJ
ma-207	111	3	there	there	PRON
ma-207	111	4	exist	exist	VERB
ma-207	111	5	constants	constant	NOUN
ma-207	111	6	γ0	γ0	NOUN
ma-207	111	7	>	>	X
ma-207	111	8	0	0	PUNCT
ma-207	112	1	and	and	CCONJ
ma-207	112	2	δ0	δ0	NOUN
ma-207	112	3	∈	∈	PROPN
ma-207	112	4	(	(	PUNCT
ma-207	112	5	0	0	NUM
ma-207	112	6	,	,	PUNCT
ma-207	112	7	1	1	NUM
ma-207	112	8	)	)	PUNCT
ma-207	112	9	so	so	SCONJ
ma-207	112	10	that	that	SCONJ
ma-207	112	11	gphψ	gphψ	NOUN
ma-207	112	12	∩	∩	NOUN
ma-207	112	13	(	(	PUNCT
ma-207	112	14	h[v	h[v	ADJ
ma-207	112	15	,	,	PUNCT
ma-207	112	16	γ0]×h[v	γ0]×h[v	NUM
ma-207	112	17	,	,	PUNCT
ma-207	112	18	δ0	δ0	NOUN
ma-207	112	19	]	]	PUNCT
ma-207	112	20	)	)	PUNCT
ma-207	112	21	is	be	AUX
ma-207	112	22	a	a	DET
ma-207	112	23	closed	closed	ADJ
ma-207	112	24	set	set	NOUN
ma-207	112	25	:	:	PUNCT
ma-207	112	26	(	(	PUNCT
ma-207	112	27	i	i	NOUN
ma-207	112	28	)	)	PUNCT
ma-207	112	29	d(v	d(v	PROPN
ma-207	112	30	,	,	PUNCT
ma-207	112	31	ψ(v	ψ(v	PROPN
ma-207	112	32	)	)	PUNCT
ma-207	112	33	)	)	PUNCT
ma-207	112	34	≤	≤	NOUN
ma-207	112	35	γ0(1−	γ0(1−	PROPN
ma-207	112	36	δ0	δ0	NOUN
ma-207	112	37	)	)	PUNCT
ma-207	112	38	and	and	CCONJ
ma-207	112	39	(	(	PUNCT
ma-207	112	40	ii	ii	NOUN
ma-207	112	41	)	)	PUNCT
ma-207	112	42	e(ψ(v1	e(ψ(v1	PROPN
ma-207	112	43	)	)	PUNCT
ma-207	112	44	∩	∩	NOUN
ma-207	112	45	h[v	h[v	ADJ
ma-207	112	46	,	,	PUNCT
ma-207	112	47	γ0],ψ(v2	γ0],ψ(v2	PROPN
ma-207	112	48	)	)	PUNCT
ma-207	112	49	)	)	PUNCT
ma-207	113	1	≤	≤	NUM
ma-207	113	2	δ0m(v1	δ0m(v1	NOUN
ma-207	113	3	,	,	PUNCT
ma-207	113	4	v2	v2	PROPN
ma-207	113	5	)	)	PUNCT
ma-207	113	6	for	for	ADP
ma-207	113	7	each	each	DET
ma-207	113	8	v1	v1	NOUN
ma-207	113	9	,	,	PUNCT
ma-207	113	10	v2	v2	PROPN
ma-207	113	11	∈	∈	PROPN
ma-207	113	12	h[v	h[v	ADJ
ma-207	113	13	,	,	PUNCT
ma-207	113	14	γ0	γ0	PROPN
ma-207	113	15	]	]	PUNCT
ma-207	113	16	,	,	PUNCT
ma-207	113	17	where	where	SCONJ
ma-207	113	18	m	m	NOUN
ma-207	113	19	is	be	AUX
ma-207	113	20	some	some	DET
ma-207	113	21	metric	metric	NOUN
ma-207	113	22	.	.	PUNCT
ma-207	114	1	then	then	ADV
ma-207	114	2	,	,	PUNCT
ma-207	114	3	the	the	DET
ma-207	114	4	operator	operator	NOUN
ma-207	114	5	ψ	ψ	PART
ma-207	114	6	admit	admit	VERB
ma-207	114	7	a	a	DET
ma-207	114	8	fixed	fix	VERB
ma-207	114	9	point	point	NOUN
ma-207	114	10	in	in	ADP
ma-207	114	11	the	the	DET
ma-207	114	12	closed	closed	ADJ
ma-207	114	13	ball	ball	NOUN
ma-207	114	14	h[v	h[v	ADJ
ma-207	114	15	,	,	PUNCT
ma-207	114	16	γ0	γ0	PROPN
ma-207	114	17	]	]	PUNCT
ma-207	114	18	.	.	PUNCT
ma-207	115	1	majorizing	majorize	VERB
ma-207	115	2	sequences	sequence	NOUN
ma-207	115	3	play	play	VERB
ma-207	115	4	an	an	DET
ma-207	115	5	important	important	ADJ
ma-207	115	6	role	role	NOUN
ma-207	115	7	in	in	ADP
ma-207	115	8	the	the	DET
ma-207	115	9	study	study	NOUN
ma-207	115	10	of	of	ADP
ma-207	115	11	iterative	iterative	ADJ
ma-207	115	12	methods	method	NOUN
ma-207	115	13	.	.	PUNCT
ma-207	116	1	definition	definition	NOUN
ma-207	116	2	2.3	2.3	NUM
ma-207	116	3	.	.	PUNCT
ma-207	117	1	let	let	AUX
ma-207	117	2	{	{	PUNCT
ma-207	117	3	sn	sn	NOUN
ma-207	117	4	}	}	PUNCT
ma-207	117	5	stand	stand	VERB
ma-207	117	6	for	for	ADP
ma-207	117	7	a	a	DET
ma-207	117	8	nonnegative	nonnegative	ADJ
ma-207	117	9	sequence	sequence	NOUN
ma-207	117	10	of	of	ADP
ma-207	117	11	numbers	number	NOUN
ma-207	117	12	and	and	CCONJ
ma-207	117	13	let	let	VERB
ma-207	117	14	{	{	PUNCT
ma-207	117	15	zn	zn	PART
ma-207	117	16	}	}	PUNCT
ma-207	117	17	be	be	AUX
ma-207	117	18	a	a	DET
ma-207	117	19	sequence	sequence	NOUN
ma-207	117	20	in	in	ADP
ma-207	117	21	a	a	DET
ma-207	117	22	banach	banach	NOUN
ma-207	117	23	space	space	NOUN
ma-207	117	24	.	.	PUNCT
ma-207	118	1	assume	assume	VERB
ma-207	118	2	:	:	PUNCT
ma-207	118	3	‖zn+1	‖zn+1	VERB
ma-207	118	4	−	−	PROPN
ma-207	118	5	zn‖	zn‖	PROPN
ma-207	118	6	≤	≤	PROPN
ma-207	118	7	sn+1	sn+1	VERB
ma-207	118	8	−	−	PROPN
ma-207	118	9	sn	sn	PROPN
ma-207	118	10	for	for	ADP
ma-207	118	11	each	each	DET
ma-207	118	12	n	n	NOUN
ma-207	118	13	=	=	SYM
ma-207	118	14	0	0	NUM
ma-207	118	15	,	,	PUNCT
ma-207	118	16	1	1	NUM
ma-207	118	17	,	,	PUNCT
ma-207	118	18	2	2	NUM
ma-207	118	19	.	.	PUNCT
ma-207	118	20	.	.	PUNCT
ma-207	118	21	.	.	PUNCT
ma-207	118	22	.	.	PUNCT
ma-207	119	1	then	then	ADV
ma-207	119	2	,	,	PUNCT
ma-207	119	3	the	the	DET
ma-207	119	4	sequence	sequence	NOUN
ma-207	119	5	{	{	PUNCT
ma-207	119	6	sn	sn	NOUN
ma-207	119	7	}	}	PUNCT
ma-207	119	8	is	be	AUX
ma-207	119	9	said	say	VERB
ma-207	119	10	to	to	PART
ma-207	119	11	be	be	AUX
ma-207	119	12	majorizing	majorize	VERB
ma-207	119	13	for	for	ADP
ma-207	119	14	the	the	DET
ma-207	119	15	sequence	sequence	NOUN
ma-207	119	16	{	{	PUNCT
ma-207	119	17	yn	yn	NOUN
ma-207	119	18	}	}	PUNCT
ma-207	119	19	.	.	PUNCT
ma-207	120	1	in	in	ADP
ma-207	120	2	the	the	DET
ma-207	120	3	case	case	NOUN
ma-207	120	4	of	of	ADP
ma-207	120	5	convergence	convergence	NOUN
ma-207	120	6	of	of	ADP
ma-207	120	7	the	the	DET
ma-207	120	8	sequence	sequence	NOUN
ma-207	120	9	{	{	PUNCT
ma-207	120	10	sn	sn	PROPN
ma-207	120	11	}	}	PUNCT
ma-207	120	12	,	,	PUNCT
ma-207	120	13	the	the	DET
ma-207	120	14	sequence	sequence	NOUN
ma-207	120	15	{	{	PUNCT
ma-207	120	16	zn	zn	NOUN
ma-207	120	17	}	}	PUNCT
ma-207	120	18	is	be	AUX
ma-207	120	19	cauchy	cauchy	ADJ
ma-207	120	20	in	in	ADP
ma-207	120	21	the	the	DET
ma-207	120	22	banach	banach	NOUN
ma-207	120	23	space	space	NOUN
ma-207	120	24	and	and	CCONJ
ma-207	120	25	as	as	ADP
ma-207	120	26	such	such	ADJ
ma-207	120	27	it	it	PRON
ma-207	120	28	is	be	AUX
ma-207	120	29	convergent	convergent	ADJ
ma-207	120	30	to	to	ADP
ma-207	120	31	some	some	DET
ma-207	120	32	z∗	z∗	NOUN
ma-207	120	33	,	,	PUNCT
ma-207	120	34	i.e.	i.e.	X
ma-207	120	35	,	,	PUNCT
ma-207	120	36	limn−→∞	limn−→∞	PROPN
ma-207	120	37	zn	zn	PROPN
ma-207	120	38	=	=	SYM
ma-207	120	39	z∗.	z∗.	PROPN
ma-207	120	40	3	3	X
ma-207	120	41	.	.	X
ma-207	120	42	convergence	convergence	NOUN
ma-207	120	43	let	let	VERB
ma-207	120	44	t	t	NOUN
ma-207	120	45	=	=	PUNCT
ma-207	121	1	[	[	X
ma-207	121	2	0,+∞	0,+∞	NUM
ma-207	121	3	)	)	PUNCT
ma-207	121	4	.	.	PUNCT
ma-207	122	1	the	the	DET
ma-207	122	2	following	follow	VERB
ma-207	122	3	conditions	condition	NOUN
ma-207	122	4	are	be	AUX
ma-207	122	5	used	use	VERB
ma-207	122	6	in	in	ADP
ma-207	122	7	the	the	DET
ma-207	122	8	semi	semi	ADJ
ma-207	122	9	-	-	ADJ
ma-207	122	10	local	local	ADJ
ma-207	122	11	convergence	convergence	NOUN
ma-207	122	12	analysis	analysis	NOUN
ma-207	122	13	ofthe	ofthe	NOUN
ma-207	122	14	nlm.assume:(a1	nlm.assume:(a1	NOUN
ma-207	122	15	)	)	PUNCT
ma-207	122	16	there	there	PRON
ma-207	122	17	exists	exist	VERB
ma-207	122	18	a	a	DET
ma-207	122	19	continuous	continuous	ADJ
ma-207	122	20	and	and	CCONJ
ma-207	122	21	nondecreasing	nondecreasing	ADJ
ma-207	122	22	function	function	NOUN
ma-207	122	23	w0	w0	PROPN
ma-207	122	24	:	:	PUNCT
ma-207	122	25	t	t	X
ma-207	122	26	−→	−→	NOUN
ma-207	122	27	r	r	NOUN
ma-207	122	28	such	such	ADJ
ma-207	122	29	that	that	SCONJ
ma-207	122	30	the	the	DET
ma-207	122	31	equation	equation	NOUN
ma-207	122	32	w0(t)−	w0(t)−	PROPN
ma-207	122	33	1	1	NUM
ma-207	122	34	=	=	SYM
ma-207	122	35	0	0	PROPN
ma-207	122	36	has	have	VERB
ma-207	122	37	a	a	DET
ma-207	122	38	smallest	small	ADJ
ma-207	122	39	solution	solution	NOUN
ma-207	122	40	ρ0	ρ0	PROPN
ma-207	122	41	∈	∈	PROPN
ma-207	122	42	t	t	PROPN
ma-207	122	43	−	−	PROPN
ma-207	122	44	{	{	PUNCT
ma-207	122	45	0	0	NUM
ma-207	122	46	}	}	PUNCT
ma-207	122	47	.	.	PUNCT
ma-207	123	1	set	set	VERB
ma-207	123	2	t0	t0	NOUN
ma-207	123	3	=	=	PUNCT
ma-207	124	1	[	[	X
ma-207	124	2	0	0	NUM
ma-207	124	3	,	,	PUNCT
ma-207	124	4	ρ0	ρ0	PROPN
ma-207	124	5	)	)	PUNCT
ma-207	124	6	.	.	PUNCT
ma-207	125	1	https://doi.org/10.28924/ada/ma.4.3	https://doi.org/10.28924/ada/ma.4.3	PROPN
ma-207	125	2	eur	eur	PROPN
ma-207	125	3	.	.	PUNCT
ma-207	126	1	j.	j.	PROPN
ma-207	126	2	math	math	PROPN
ma-207	126	3	.	.	PUNCT
ma-207	127	1	anal	anal	PROPN
ma-207	127	2	.	.	PUNCT
ma-207	128	1	10.28924	10.28924	NUM
ma-207	128	2	/	/	SYM
ma-207	128	3	ada	ada	PROPN
ma-207	128	4	/	/	SYM
ma-207	128	5	ma.4.3	ma.4.3	PROPN
ma-207	128	6	5(a2	5(a2	NOUN
ma-207	128	7	)	)	PUNCT
ma-207	128	8	there	there	PRON
ma-207	128	9	exist	exist	VERB
ma-207	128	10	cnf	cnf	PROPN
ma-207	128	11	w	w	PROPN
ma-207	128	12	:	:	PUNCT
ma-207	128	13	t0	t0	VERB
ma-207	128	14	−→	−→	ADJ
ma-207	128	15	r	r	NOUN
ma-207	128	16	,	,	PUNCT
ma-207	128	17	and	and	CCONJ
ma-207	128	18	w1	w1	NOUN
ma-207	128	19	:	:	PUNCT
ma-207	128	20	t	t	PROPN
ma-207	128	21	−→	−→	PROPN
ma-207	128	22	r.	r.	PROPN
ma-207	128	23	let	let	VERB
ma-207	128	24	λ	λ	PROPN
ma-207	128	25	>	>	X
ma-207	128	26	0	0	X
ma-207	128	27	.	.	PUNCT
ma-207	128	28	define	define	VERB
ma-207	128	29	the	the	DET
ma-207	128	30	sequence	sequence	NOUN
ma-207	128	31	{	{	PUNCT
ma-207	128	32	sn}for	sn}for	ADP
ma-207	128	33	s0	s0	NOUN
ma-207	128	34	=	=	SYM
ma-207	128	35	0	0	NUM
ma-207	128	36	,	,	PUNCT
ma-207	128	37	some	some	DET
ma-207	128	38	s1	s1	PROPN
ma-207	128	39	∈	∈	PROPN
ma-207	129	1	[	[	X
ma-207	129	2	0	0	NUM
ma-207	129	3	,	,	PUNCT
ma-207	129	4	ρ0	ρ0	PROPN
ma-207	129	5	)	)	PUNCT
ma-207	129	6	,	,	PUNCT
ma-207	129	7	and	and	CCONJ
ma-207	129	8	each	each	DET
ma-207	129	9	n	n	NOUN
ma-207	129	10	=	=	SYM
ma-207	129	11	0	0	NUM
ma-207	129	12	,	,	PUNCT
ma-207	129	13	1	1	NUM
ma-207	129	14	,	,	PUNCT
ma-207	129	15	2	2	NUM
ma-207	129	16	,	,	PUNCT
ma-207	129	17	...	...	PUNCT
ma-207	129	18	by	by	ADP
ma-207	129	19	sn+1	sn+1	PROPN
ma-207	129	20	=	=	SYM
ma-207	129	21	sn	sn	PROPN
ma-207	130	1	+	+	CCONJ
ma-207	130	2	[	[	PUNCT
ma-207	130	3	∫	∫	PROPN
ma-207	130	4	1	1	NUM
ma-207	130	5	0	0	NUM
ma-207	130	6	w((1−	w((1−	X
ma-207	130	7	θ)(sn	θ)(sn	VERB
ma-207	130	8	−	−	PROPN
ma-207	130	9	sn−1))dθ	sn−1))dθ	NOUN
ma-207	130	10	+	+	CCONJ
ma-207	130	11	w0(sn−1	w0(sn−1	NUM
ma-207	130	12	)	)	PUNCT
ma-207	131	1	+	+	CCONJ
ma-207	131	2	w1(sn−1)](sn	w1(sn−1)](sn	VERB
ma-207	131	3	−	−	PUNCT
ma-207	131	4	sn−1	sn−1	PROPN
ma-207	131	5	)	)	PUNCT
ma-207	131	6	1−	1−	NUM
ma-207	131	7	w0(sn	w0(sn	PROPN
ma-207	131	8	)	)	PUNCT
ma-207	131	9	(	(	PUNCT
ma-207	131	10	3.1	3.1	NUM
ma-207	131	11	)	)	PUNCT
ma-207	131	12	it	it	PRON
ma-207	131	13	is	be	AUX
ma-207	131	14	shown	show	VERB
ma-207	131	15	in	in	ADP
ma-207	131	16	theorem	theorem	ADJ
ma-207	131	17	3.1	3.1	NUM
ma-207	131	18	that	that	SCONJ
ma-207	131	19	{	{	PUNCT
ma-207	131	20	sn	sn	NOUN
ma-207	131	21	}	}	PUNCT
ma-207	131	22	is	be	AUX
ma-207	131	23	a	a	DET
ma-207	131	24	majorizing	majorize	VERB
ma-207	131	25	sequence	sequence	NOUN
ma-207	131	26	for	for	ADP
ma-207	131	27	{	{	PUNCT
ma-207	131	28	xn	xn	NOUN
ma-207	131	29	}	}	PUNCT
ma-207	131	30	.	.	PUNCT
ma-207	132	1	but	but	CCONJ
ma-207	132	2	let	let	VERB
ma-207	132	3	us	we	PRON
ma-207	132	4	firstpresent	firstpresent	VERB
ma-207	132	5	a	a	DET
ma-207	132	6	general	general	ADJ
ma-207	132	7	convergence	convergence	NOUN
ma-207	132	8	criterion	criterion	NOUN
ma-207	132	9	for	for	ADP
ma-207	132	10	it.(a3	it.(a3	PROPN
ma-207	132	11	)	)	PUNCT
ma-207	132	12	there	there	PRON
ma-207	132	13	exists	exist	VERB
ma-207	132	14	a	a	DET
ma-207	132	15	parameter	parameter	NOUN
ma-207	132	16	ρ	ρ	PROPN
ma-207	132	17	∈	∈	PROPN
ma-207	133	1	[	[	X
ma-207	133	2	0	0	NUM
ma-207	133	3	,	,	PUNCT
ma-207	133	4	ρ0	ρ0	PROPN
ma-207	133	5	)	)	PUNCT
ma-207	133	6	such	such	ADJ
ma-207	133	7	that	that	PRON
ma-207	133	8	for	for	ADP
ma-207	133	9	each	each	DET
ma-207	133	10	n	n	NOUN
ma-207	133	11	=	=	SYM
ma-207	133	12	0	0	NUM
ma-207	133	13	,	,	PUNCT
ma-207	133	14	1	1	NUM
ma-207	133	15	,	,	PUNCT
ma-207	133	16	2	2	NUM
ma-207	133	17	,	,	PUNCT
ma-207	133	18	...	...	PUNCT
ma-207	134	1	w0(sn	w0(sn	PROPN
ma-207	134	2	)	)	PUNCT
ma-207	134	3	<	<	X
ma-207	134	4	1	1	NUM
ma-207	134	5	and	and	CCONJ
ma-207	134	6	sn	sn	PROPN
ma-207	134	7	≤	≤	NOUN
ma-207	134	8	ρ.it	ρ.it	NOUN
ma-207	134	9	follows	follow	VERB
ma-207	134	10	by	by	ADP
ma-207	134	11	(	(	PUNCT
ma-207	134	12	3.1	3.1	NUM
ma-207	134	13	)	)	PUNCT
ma-207	134	14	and	and	CCONJ
ma-207	134	15	(	(	PUNCT
ma-207	134	16	a3	a3	NOUN
ma-207	134	17	)	)	PUNCT
ma-207	134	18	that	that	SCONJ
ma-207	134	19	0	0	NUM
ma-207	134	20	≤	≤	NUM
ma-207	134	21	sn	sn	PROPN
ma-207	134	22	≤	≤	NUM
ma-207	134	23	sn+1	sn+1	VERB
ma-207	134	24	≤	≤	NUM
ma-207	134	25	ρand	ρand	NOUN
ma-207	134	26	there	there	PRON
ma-207	134	27	exists	exist	VERB
ma-207	134	28	s	s	X
ma-207	134	29	∈	∈	PROPN
ma-207	135	1	[	[	X
ma-207	135	2	0	0	NUM
ma-207	135	3	,	,	PUNCT
ma-207	135	4	ρ	ρ	NOUN
ma-207	135	5	)	)	PUNCT
ma-207	135	6	such	such	ADJ
ma-207	135	7	that	that	PRON
ma-207	135	8	limn→+∞	limn→+∞	VERB
ma-207	135	9	sn	sn	PROPN
ma-207	135	10	=	=	SYM
ma-207	135	11	s	s	PART
ma-207	135	12	.the	.the	NOUN
ma-207	135	13	functions	function	NOUN
ma-207	135	14	"	"	PUNCT
ma-207	135	15	w	w	NOUN
ma-207	135	16	"	"	PUNCT
ma-207	135	17	and	and	CCONJ
ma-207	135	18	sequence	sequence	NOUN
ma-207	135	19	{	{	PUNCT
ma-207	135	20	sn	sn	NOUN
ma-207	135	21	}	}	PUNCT
ma-207	135	22	are	be	AUX
ma-207	135	23	connected	connect	VERB
ma-207	135	24	to	to	ADP
ma-207	135	25	the	the	DET
ma-207	135	26	operators	operator	NOUN
ma-207	135	27	on	on	ADP
ma-207	135	28	nlm.(a4	nlm.(a4	PROPN
ma-207	135	29	)	)	PUNCT
ma-207	136	1	there	there	PRON
ma-207	136	2	exists	exist	VERB
ma-207	136	3	a	a	DET
ma-207	136	4	linear	linear	ADJ
ma-207	136	5	operator	operator	NOUN
ma-207	136	6	m	m	VERB
ma-207	136	7	such	such	ADJ
ma-207	136	8	that	that	SCONJ
ma-207	136	9	λ‖l(x)−m‖	λ‖l(x)−m‖	PROPN
ma-207	136	10	≤	≤	NUM
ma-207	137	1	w0(‖x	w0(‖x	CCONJ
ma-207	137	2	−	−	PROPN
ma-207	137	3	x0‖	x0‖	PROPN
ma-207	137	4	)	)	PUNCT
ma-207	137	5	for	for	ADP
ma-207	137	6	each	each	DET
ma-207	137	7	x	x	SYM
ma-207	137	8	∈	∈	PROPN
ma-207	137	9	d.set	d.set	NOUN
ma-207	137	10	d0	d0	NOUN
ma-207	137	11	=	=	SYM
ma-207	138	1	d	d	PROPN
ma-207	138	2	∩	∩	X
ma-207	138	3	s(x0	s(x0	NOUN
ma-207	138	4	,	,	PUNCT
ma-207	138	5	ρ0).(a5	ρ0).(a5	ADV
ma-207	138	6	)	)	PUNCT
ma-207	138	7	λ‖f	λ‖f	PROPN
ma-207	138	8	′(x)−	′(x)−	PROPN
ma-207	138	9	f	f	PROPN
ma-207	138	10	′(y)‖	′(y)‖	PROPN
ma-207	138	11	≤	≤	PROPN
ma-207	138	12	w(‖x	w(‖x	PUNCT
ma-207	138	13	−	−	PROPN
ma-207	138	14	y‖	y‖	PROPN
ma-207	138	15	)	)	PUNCT
ma-207	138	16	for	for	ADP
ma-207	138	17	each	each	DET
ma-207	138	18	x	x	NOUN
ma-207	138	19	,	,	PUNCT
ma-207	138	20	y	y	PROPN
ma-207	138	21	∈	∈	PROPN
ma-207	138	22	d0	d0	NOUN
ma-207	138	23	and	and	CCONJ
ma-207	138	24	λ‖l(x)−m‖	λ‖l(x)−m‖	PROPN
ma-207	138	25	≤	≤	NUM
ma-207	138	26	w1(‖x	w1(‖x	PROPN
ma-207	138	27	−	−	PROPN
ma-207	138	28	x0‖	x0‖	PROPN
ma-207	138	29	)	)	PUNCT
ma-207	138	30	for	for	ADP
ma-207	138	31	each	each	DET
ma-207	138	32	x	x	SYM
ma-207	138	33	∈	∈	NOUN
ma-207	138	34	d0.(a6	d0.(a6	NOUN
ma-207	138	35	)	)	PUNCT
ma-207	138	36	there	there	PRON
ma-207	138	37	exist	exist	VERB
ma-207	139	1	x1	x1	PROPN
ma-207	139	2	∈	∈	PROPN
ma-207	140	1	d	d	NOUN
ma-207	141	1	generated	generate	VERB
ma-207	141	2	by	by	ADP
ma-207	141	3	nlm	nlm	PROPN
ma-207	141	4	so	so	SCONJ
ma-207	141	5	that	that	SCONJ
ma-207	141	6	‖x1	‖x1	NOUN
ma-207	141	7	−	−	PROPN
ma-207	141	8	x0‖	x0‖	PROPN
ma-207	141	9	≤	≤	NUM
ma-207	141	10	s1	s1	NOUN
ma-207	141	11	,	,	PUNCT
ma-207	141	12	and	and	CCONJ
ma-207	141	13	the	the	DET
ma-207	141	14	multi	multi	NOUN
ma-207	141	15	-	-	NOUN
ma-207	141	16	operator	operator	NOUN
ma-207	141	17	(	(	PUNCT
ma-207	141	18	f	f	X
ma-207	141	19	(	(	PUNCT
ma-207	141	20	x0	x0	PROPN
ma-207	141	21	)	)	PUNCT
ma-207	142	1	+	+	VERB
ma-207	142	2	m(.−	m(.−	ADJ
ma-207	142	3	x0	x0	NOUN
ma-207	142	4	)	)	PUNCT
ma-207	143	1	+	+	PUNCT
ma-207	143	2	g(.))−1	g(.))−1	X
ma-207	143	3	is	be	AUX
ma-207	143	4	aubin	aubin	PROPN
ma-207	143	5	continuous	continuous	ADJ
ma-207	143	6	at	at	ADP
ma-207	143	7	(	(	PUNCT
ma-207	143	8	0	0	NUM
ma-207	143	9	,	,	PUNCT
ma-207	143	10	x1	x1	NUM
ma-207	143	11	)	)	PUNCT
ma-207	143	12	with	with	ADP
ma-207	143	13	corresponding	correspond	VERB
ma-207	143	14	parameters	parameter	NOUN
ma-207	143	15	α	α	NOUN
ma-207	143	16	and	and	CCONJ
ma-207	143	17	β.(a7	β.(a7	NUM
ma-207	143	18	)	)	PUNCT
ma-207	143	19	for	for	ADP
ma-207	143	20	ρ	ρ	PROPN
ma-207	143	21	>	>	X
ma-207	143	22	s1	s1	PROPN
ma-207	143	23	2ρ−	2ρ−	PROPN
ma-207	143	24	s1	s1	PROPN
ma-207	143	25	<	<	X
ma-207	143	26	α	α	PROPN
ma-207	143	27	,	,	PUNCT
ma-207	143	28	1	1	NUM
ma-207	143	29	λ	λ	NOUN
ma-207	144	1	[	[	X
ma-207	144	2	∫	∫	PROPN
ma-207	144	3	1	1	NUM
ma-207	144	4	0	0	NUM
ma-207	144	5	w0((1−	w0((1−	NOUN
ma-207	144	6	θ)ρ)dθ	θ)ρ)dθ	PART
ma-207	144	7	+	+	CCONJ
ma-207	144	8	w0(ρ	w0(ρ	NOUN
ma-207	144	9	)	)	PUNCT
ma-207	145	1	+	+	CCONJ
ma-207	145	2	∫	∫	PROPN
ma-207	145	3	1	1	NUM
ma-207	145	4	0	0	NUM
ma-207	145	5	w((1−	w((1−	NUM
ma-207	145	6	θ)ρ)dθ	θ)ρ)dθ	X
ma-207	145	7	+	+	CCONJ
ma-207	145	8	w1(ρ	w1(ρ	NOUN
ma-207	145	9	)	)	PUNCT
ma-207	145	10	]	]	PUNCT
ma-207	146	1	ρ	ρ	X
ma-207	146	2	≤	≤	NUM
ma-207	146	3	β	β	NOUN
ma-207	146	4	,	,	PUNCT
ma-207	146	5	and	and	CCONJ
ma-207	146	6	w0(ρ	w0(ρ	NOUN
ma-207	146	7	)	)	PUNCT
ma-207	146	8	<	<	X
ma-207	146	9	1.and(a8	1.and(a8	NUM
ma-207	146	10	)	)	PUNCT
ma-207	146	11	s[x0	s[x0	NOUN
ma-207	146	12	,	,	PUNCT
ma-207	146	13	s	s	AUX
ma-207	146	14	]	]	X
ma-207	146	15	⊂	⊂	PROPN
ma-207	146	16	d.next	d.next	PROPN
ma-207	146	17	,	,	PUNCT
ma-207	146	18	the	the	DET
ma-207	146	19	semi	semi	ADJ
ma-207	146	20	-	-	ADJ
ma-207	146	21	local	local	ADJ
ma-207	146	22	convergence	convergence	NOUN
ma-207	146	23	analysis	analysis	NOUN
ma-207	146	24	of	of	ADP
ma-207	146	25	nlm	nlm	PROPN
ma-207	146	26	is	be	AUX
ma-207	146	27	developed	develop	VERB
ma-207	146	28	using	use	VERB
ma-207	146	29	the	the	DET
ma-207	146	30	conditions	condition	NOUN
ma-207	146	31	(	(	PUNCT
ma-207	146	32	a1)−	a1)−	PROPN
ma-207	146	33	(	(	PUNCT
ma-207	146	34	a8	a8	PROPN
ma-207	146	35	)	)	PUNCT
ma-207	146	36	.	.	PUNCT
ma-207	147	1	theorem	theorem	VERB
ma-207	147	2	3.1	3.1	NUM
ma-207	147	3	.	.	PUNCT
ma-207	148	1	assume	assume	VERB
ma-207	148	2	that	that	SCONJ
ma-207	148	3	the	the	DET
ma-207	148	4	conditions	condition	NOUN
ma-207	148	5	(	(	PUNCT
ma-207	148	6	a1	a1	NOUN
ma-207	148	7	)	)	PUNCT
ma-207	148	8	−	−	PROPN
ma-207	148	9	(	(	PUNCT
ma-207	148	10	a8	a8	PROPN
ma-207	148	11	)	)	PUNCT
ma-207	148	12	are	be	AUX
ma-207	148	13	valid	valid	ADJ
ma-207	148	14	.	.	PUNCT
ma-207	149	1	then	then	ADV
ma-207	149	2	,	,	PUNCT
ma-207	149	3	the	the	DET
ma-207	149	4	sequence	sequence	NOUN
ma-207	149	5	{	{	PUNCT
ma-207	149	6	xn	xn	PROPN
ma-207	149	7	}	}	PUNCT
ma-207	149	8	generated	generate	VERB
ma-207	149	9	by	by	ADP
ma-207	149	10	nlm	nlm	PROPN
ma-207	149	11	is	be	AUX
ma-207	149	12	well	well	ADV
ma-207	149	13	defined	define	VERB
ma-207	149	14	in	in	ADP
ma-207	149	15	s(x0	s(x0	PROPN
ma-207	149	16	,	,	PUNCT
ma-207	149	17	s	s	PROPN
ma-207	149	18	)	)	PUNCT
ma-207	149	19	,	,	PUNCT
ma-207	149	20	remains	remain	VERB
ma-207	149	21	in	in	ADP
ma-207	149	22	s(x0	s(x0	PROPN
ma-207	149	23	,	,	PUNCT
ma-207	149	24	s	s	PROPN
ma-207	149	25	)	)	PUNCT
ma-207	149	26	for	for	ADP
ma-207	149	27	each	each	DET
ma-207	149	28	n	n	NOUN
ma-207	149	29	=	=	SYM
ma-207	149	30	0	0	NUM
ma-207	149	31	,	,	PUNCT
ma-207	149	32	1	1	NUM
ma-207	149	33	,	,	PUNCT
ma-207	149	34	2	2	NUM
ma-207	149	35	,	,	PUNCT
ma-207	149	36	..	..	PUNCT
ma-207	149	37	and	and	CCONJ
ma-207	149	38	is	be	AUX
ma-207	149	39	convergent	convergent	ADJ
ma-207	149	40	to	to	ADP
ma-207	149	41	some	some	DET
ma-207	149	42	x∗	x∗	PROPN
ma-207	149	43	∈	∈	PROPN
ma-207	149	44	s[x0	s[x0	NOUN
ma-207	149	45	,	,	PUNCT
ma-207	149	46	s	s	AUX
ma-207	149	47	]	]	PUNCT
ma-207	149	48	solving	solve	VERB
ma-207	149	49	the	the	DET
ma-207	149	50	generalized	generalized	ADJ
ma-207	149	51	equation	equation	NOUN
ma-207	149	52	(	(	PUNCT
ma-207	149	53	1.1	1.1	NUM
ma-207	149	54	)	)	PUNCT
ma-207	149	55	.	.	PUNCT
ma-207	150	1	moreover	moreover	ADV
ma-207	150	2	,	,	PUNCT
ma-207	150	3	the	the	DET
ma-207	150	4	following	follow	VERB
ma-207	150	5	error	error	NOUN
ma-207	150	6	estimates	estimate	NOUN
ma-207	150	7	hold	hold	VERB
ma-207	150	8	for	for	ADP
ma-207	150	9	each	each	DET
ma-207	150	10	n	n	NOUN
ma-207	150	11	=	=	SYM
ma-207	150	12	0	0	NUM
ma-207	150	13	,	,	PUNCT
ma-207	150	14	1	1	NUM
ma-207	150	15	,	,	PUNCT
ma-207	150	16	2	2	NUM
ma-207	150	17	,	,	PUNCT
ma-207	150	18	...	...	PUNCT
ma-207	150	19	‖x∗	‖x∗	PUNCT
ma-207	151	1	−	−	NOUN
ma-207	151	2	xn‖	xn‖	PROPN
ma-207	151	3	≤	≤	PROPN
ma-207	151	4	s	s	PART
ma-207	151	5	−	−	PROPN
ma-207	151	6	sn	sn	PROPN
ma-207	151	7	.	.	PUNCT
ma-207	152	1	(	(	PUNCT
ma-207	152	2	3.2	3.2	NUM
ma-207	152	3	)	)	PUNCT
ma-207	152	4	https://doi.org/10.28924/ada/ma.4.3	https://doi.org/10.28924/ada/ma.4.3	PROPN
ma-207	152	5	eur	eur	PROPN
ma-207	152	6	.	.	PUNCT
ma-207	153	1	j.	j.	PROPN
ma-207	153	2	math	math	PROPN
ma-207	153	3	.	.	PUNCT
ma-207	154	1	anal	anal	PROPN
ma-207	154	2	.	.	PUNCT
ma-207	155	1	10.28924	10.28924	NUM
ma-207	155	2	/	/	SYM
ma-207	155	3	ada	ada	PROPN
ma-207	155	4	/	/	SYM
ma-207	155	5	ma.4.3	ma.4.3	PROPN
ma-207	155	6	6	6	NUM
ma-207	155	7	proof	proof	NOUN
ma-207	155	8	.	.	PUNCT
ma-207	156	1	mathematical	mathematical	ADJ
ma-207	156	2	induction	induction	NOUN
ma-207	156	3	is	be	AUX
ma-207	156	4	employed	employ	VERB
ma-207	156	5	to	to	PART
ma-207	156	6	show	show	VERB
ma-207	156	7	the	the	DET
ma-207	156	8	assertion	assertion	NOUN
ma-207	156	9	for	for	ADP
ma-207	156	10	each	each	DET
ma-207	156	11	n	n	NOUN
ma-207	156	12	=	=	SYM
ma-207	156	13	0	0	NUM
ma-207	156	14	,	,	PUNCT
ma-207	156	15	1	1	NUM
ma-207	156	16	,	,	PUNCT
ma-207	156	17	2	2	NUM
ma-207	156	18	,	,	PUNCT
ma-207	156	19	...	...	PUNCT
ma-207	157	1	‖xn+1	‖xn+1	NUM
ma-207	157	2	−	−	NOUN
ma-207	157	3	xn‖	xn‖	PROPN
ma-207	157	4	≤	≤	PROPN
ma-207	157	5	sn+1	sn+1	VERB
ma-207	157	6	−	−	PROPN
ma-207	157	7	sn	sn	PROPN
ma-207	157	8	<	<	X
ma-207	157	9	s	s	X
ma-207	157	10	(	(	PUNCT
ma-207	157	11	3.3	3.3	NUM
ma-207	157	12	)	)	PUNCT
ma-207	157	13	the	the	DET
ma-207	157	14	assertion	assertion	NOUN
ma-207	157	15	(	(	PUNCT
ma-207	157	16	3.3	3.3	NUM
ma-207	157	17	)	)	PUNCT
ma-207	157	18	holds	hold	VERB
ma-207	157	19	for	for	ADP
ma-207	157	20	n	n	NOUN
ma-207	157	21	=	=	SYM
ma-207	157	22	0	0	NUM
ma-207	157	23	by	by	ADP
ma-207	157	24	(	(	PUNCT
ma-207	157	25	a2	a2	PROPN
ma-207	157	26	)	)	PUNCT
ma-207	157	27	and	and	CCONJ
ma-207	157	28	the	the	DET
ma-207	157	29	definition	definition	NOUN
ma-207	157	30	of	of	ADP
ma-207	157	31	s1	s1	PROPN
ma-207	157	32	in	in	ADP
ma-207	157	33	(	(	PUNCT
ma-207	157	34	a6	a6	NOUN
ma-207	157	35	)	)	PUNCT
ma-207	157	36	.	.	PUNCT
ma-207	158	1	let	let	VERB
ma-207	158	2	us	we	PRON
ma-207	158	3	assume	assume	VERB
ma-207	158	4	thatthere	thatthere	NOUN
ma-207	158	5	exist	exist	VERB
ma-207	158	6	x1	x1	PROPN
ma-207	158	7	,	,	PUNCT
ma-207	158	8	...	...	PUNCT
ma-207	158	9	,	,	PUNCT
ma-207	158	10	xm	xm	PROPN
ma-207	158	11	generated	generate	VERB
ma-207	158	12	by	by	ADP
ma-207	158	13	nlm	nlm	PROPN
ma-207	158	14	satisfying	satisfying	NOUN
ma-207	158	15	for	for	ADP
ma-207	158	16	all	all	DET
ma-207	158	17	integers	integer	NOUN
ma-207	158	18	m	m	VERB
ma-207	158	19	=	=	SYM
ma-207	158	20	0	0	NUM
ma-207	158	21	,	,	PUNCT
ma-207	158	22	1	1	NUM
ma-207	158	23	,	,	PUNCT
ma-207	158	24	2	2	NUM
ma-207	158	25	,	,	PUNCT
ma-207	158	26	...	...	PUNCT
ma-207	158	27	,	,	PUNCT
ma-207	159	1	n	n	CCONJ
ma-207	159	2	−	−	PROPN
ma-207	159	3	1	1	NUM
ma-207	159	4	‖xm	‖xm	PROPN
ma-207	159	5	−	−	NOUN
ma-207	159	6	xm−1‖	xm−1‖	PROPN
ma-207	159	7	≤	≤	PROPN
ma-207	159	8	sm	sm	VERB
ma-207	159	9	−	−	PROPN
ma-207	159	10	sm−1	sm−1	NOUN
ma-207	159	11	.	.	PUNCT
ma-207	160	1	then	then	ADV
ma-207	160	2	,	,	PUNCT
ma-207	160	3	‖xm	‖xm	PROPN
ma-207	160	4	−	−	PROPN
ma-207	160	5	x0‖	x0‖	PROPN
ma-207	160	6	≤	≤	PROPN
ma-207	161	1	‖xm	‖xm	PUNCT
ma-207	161	2	−	−	NOUN
ma-207	161	3	xm−1‖+	xm−1‖+	NOUN
ma-207	161	4	‖xm−1	‖xm−1	NOUN
ma-207	161	5	−	−	NOUN
ma-207	161	6	xm−2‖+	xm−2‖+	PRON
ma-207	161	7	...	...	PUNCT
ma-207	162	1	+	+	CCONJ
ma-207	162	2	‖x1	‖x1	NOUN
ma-207	162	3	−	−	PROPN
ma-207	162	4	x0‖	x0‖	PROPN
ma-207	162	5	≤	≤	PROPN
ma-207	162	6	sm	sm	VERB
ma-207	162	7	−	−	PROPN
ma-207	162	8	sm−1	sm−1	NOUN
ma-207	162	9	+	+	CCONJ
ma-207	162	10	sm−1	sm−1	NOUN
ma-207	162	11	−	−	PUNCT
ma-207	163	1	sm−2	sm−2	ADV
ma-207	163	2	+	+	CCONJ
ma-207	163	3	...	...	PUNCT
ma-207	163	4	+	+	CCONJ
ma-207	164	1	s1	s1	NOUN
ma-207	164	2	−	−	PROPN
ma-207	164	3	s0	s0	NOUN
ma-207	164	4	=	=	PUNCT
ma-207	164	5	sm	sm	X
ma-207	164	6	<	<	X
ma-207	164	7	s	s	PROPN
ma-207	164	8	,	,	PUNCT
ma-207	164	9	and	and	CCONJ
ma-207	164	10	‖xm	‖xm	PROPN
ma-207	164	11	−	−	NOUN
ma-207	165	1	x1‖	x1‖	PROPN
ma-207	165	2	≤	≤	X
ma-207	166	1	‖xm	‖xm	PUNCT
ma-207	166	2	−	−	PROPN
ma-207	167	1	x0‖+	x0‖+	NUM
ma-207	168	1	‖x0	‖x0	ADJ
ma-207	169	1	−	−	PROPN
ma-207	169	2	x1‖	x1‖	PROPN
ma-207	169	3	≤	≤	PROPN
ma-207	169	4	sm	sm	VERB
ma-207	169	5	−	−	PROPN
ma-207	169	6	s1	s1	PROPN
ma-207	169	7	≤	≤	PROPN
ma-207	169	8	s	s	PART
ma-207	169	9	−	−	PROPN
ma-207	169	10	s1	s1	PROPN
ma-207	169	11	.	.	PUNCT
ma-207	170	1	pic	pic	NOUN
ma-207	170	2	x	x	PUNCT
ma-207	170	3	∈	∈	PROPN
ma-207	170	4	u(xm	u(xm	PROPN
ma-207	170	5	,	,	PUNCT
ma-207	170	6	‖xm	‖xm	PROPN
ma-207	170	7	−	−	PROPN
ma-207	170	8	x0‖	x0‖	PROPN
ma-207	170	9	)	)	PUNCT
ma-207	170	10	to	to	PART
ma-207	170	11	be	be	AUX
ma-207	170	12	arbitrary	arbitrary	ADJ
ma-207	170	13	.	.	PUNCT
ma-207	171	1	define	define	VERB
ma-207	171	2	the	the	DET
ma-207	171	3	operator	operator	NOUN
ma-207	171	4	q	q	NOUN
ma-207	171	5	=	=	SYM
ma-207	171	6	f	f	X
ma-207	171	7	(	(	PUNCT
ma-207	171	8	x0	x0	PROPN
ma-207	171	9	)	)	PUNCT
ma-207	172	1	+	+	PROPN
ma-207	172	2	m(x	m(x	PROPN
ma-207	172	3	−	−	PROPN
ma-207	172	4	x0	x0	PROPN
ma-207	172	5	)	)	PUNCT
ma-207	173	1	+	+	CCONJ
ma-207	173	2	g(x	g(x	NOUN
ma-207	173	3	)	)	PUNCT
ma-207	173	4	,	,	PUNCT
ma-207	173	5	and	and	CCONJ
ma-207	173	6	the	the	DET
ma-207	173	7	multi	multi	ADJ
ma-207	173	8	-	-	NOUN
ma-207	173	9	operator	operator	NOUN
ma-207	173	10	ψm(x	ψm(x	NOUN
ma-207	173	11	)	)	PUNCT
ma-207	173	12	=	=	SYM
ma-207	174	1	q−1[f	q−1[f	PROPN
ma-207	174	2	(	(	PUNCT
ma-207	174	3	x0	x0	PROPN
ma-207	174	4	)	)	PUNCT
ma-207	175	1	+	+	PROPN
ma-207	175	2	m(x	m(x	PROPN
ma-207	175	3	−	−	PROPN
ma-207	176	1	x0)−	x0)−	PROPN
ma-207	176	2	f	f	PROPN
ma-207	176	3	(	(	PUNCT
ma-207	176	4	xm)−	xm)−	PROPN
ma-207	176	5	l(xm)(x	l(xm)(x	PROPN
ma-207	176	6	−	−	PROPN
ma-207	176	7	xm	xm	PROPN
ma-207	176	8	)	)	PUNCT
ma-207	176	9	]	]	PUNCT
ma-207	176	10	.	.	PUNCT
ma-207	177	1	the	the	DET
ma-207	177	2	conditions	condition	NOUN
ma-207	177	3	of	of	ADP
ma-207	177	4	the	the	DET
ma-207	177	5	theorem	theorem	NOUN
ma-207	177	6	2.2	2.2	NUM
ma-207	177	7	are	be	AUX
ma-207	177	8	validated	validate	VERB
ma-207	177	9	in	in	ADP
ma-207	177	10	turn	turn	NOUN
ma-207	177	11	next	next	ADV
ma-207	177	12	.	.	PUNCT
ma-207	178	1	by	by	ADP
ma-207	178	2	applying	apply	VERB
ma-207	178	3	the	the	DET
ma-207	178	4	conditions	condition	NOUN
ma-207	178	5	(	(	PUNCT
ma-207	178	6	a5	a5	PROPN
ma-207	178	7	)	)	PUNCT
ma-207	178	8	and(a7	and(a7	PROPN
ma-207	178	9	)	)	PUNCT
ma-207	178	10	,	,	PUNCT
ma-207	178	11	we	we	PRON
ma-207	178	12	get	get	VERB
ma-207	178	13	‖f	‖f	PRON
ma-207	178	14	(	(	PUNCT
ma-207	178	15	x0	x0	PROPN
ma-207	178	16	)	)	PUNCT
ma-207	179	1	+	+	PROPN
ma-207	179	2	m(x	m(x	PROPN
ma-207	179	3	−	−	PROPN
ma-207	180	1	x0)−	x0)−	PROPN
ma-207	180	2	f	f	PROPN
ma-207	180	3	(	(	PUNCT
ma-207	180	4	xm)−	xm)−	PROPN
ma-207	180	5	l(xm)(x	l(xm)(x	PROPN
ma-207	180	6	−	−	PROPN
ma-207	180	7	xm)‖	xm)‖	PROPN
ma-207	180	8	≤	≤	NOUN
ma-207	180	9	‖f	‖f	PRON
ma-207	180	10	(	(	PUNCT
ma-207	180	11	x)−	x)−	PROPN
ma-207	180	12	f	f	PROPN
ma-207	180	13	(	(	PUNCT
ma-207	180	14	x0)−m(x	x0)−m(x	PUNCT
ma-207	181	1	−	−	PROPN
ma-207	181	2	x0)‖	x0)‖	X
ma-207	182	1	+	+	PROPN
ma-207	182	2	‖f	‖f	ADP
ma-207	182	3	(	(	PUNCT
ma-207	182	4	x)−	x)−	PROPN
ma-207	182	5	f	f	PROPN
ma-207	182	6	(	(	PUNCT
ma-207	182	7	xm)−	xm)−	PROPN
ma-207	182	8	f	f	PROPN
ma-207	182	9	′(xm)(x	′(xm)(x	PROPN
ma-207	182	10	−	−	PROPN
ma-207	182	11	xm)‖	xm)‖	PROPN
ma-207	183	1	+	+	PROPN
ma-207	183	2	‖f	‖f	ADJ
ma-207	183	3	′(xm)−m‖‖x	′(xm)−m‖‖x	ADJ
ma-207	183	4	−	−	PROPN
ma-207	183	5	xm‖+	xm‖+	PROPN
ma-207	183	6	‖m	‖m	NOUN
ma-207	183	7	−	−	PROPN
ma-207	183	8	l(xm)‖‖x	l(xm)‖‖x	PROPN
ma-207	184	1	−	−	PROPN
ma-207	184	2	xm‖	xm‖	PROPN
ma-207	184	3	1	1	NUM
ma-207	184	4	λ	λ	NOUN
ma-207	184	5	[	[	X
ma-207	184	6	∫	∫	PROPN
ma-207	184	7	1	1	NUM
ma-207	184	8	0	0	NUM
ma-207	184	9	w0((1−	w0((1−	NOUN
ma-207	184	10	θ)‖x	θ)‖x	NOUN
ma-207	184	11	−	−	PROPN
ma-207	184	12	x0‖)dθ‖x	x0‖)dθ‖x	PROPN
ma-207	184	13	−	−	PROPN
ma-207	184	14	x0‖	x0‖	PROPN
ma-207	185	1	+	+	CCONJ
ma-207	185	2	∫	∫	PROPN
ma-207	185	3	1	1	NUM
ma-207	185	4	0	0	NUM
ma-207	185	5	w((1−	w((1−	NUM
ma-207	185	6	θ)‖x	θ)‖x	NOUN
ma-207	185	7	−	−	PROPN
ma-207	185	8	xm‖)dθ‖x	xm‖)dθ‖x	PROPN
ma-207	185	9	−	−	PROPN
ma-207	186	1	xm‖	xm‖	PROPN
ma-207	187	1	+	+	PROPN
ma-207	187	2	w0(‖xm	w0(‖xm	PROPN
ma-207	187	3	−	−	PROPN
ma-207	187	4	x0‖)‖x	x0‖)‖x	PROPN
ma-207	187	5	−	−	PROPN
ma-207	187	6	xm‖+	xm‖+	PROPN
ma-207	187	7	w1)‖xm	w1)‖xm	VERB
ma-207	187	8	−	−	PROPN
ma-207	187	9	x0‖)‖x	x0‖)‖x	NOUN
ma-207	187	10	−	−	PROPN
ma-207	188	1	xm‖	xm‖	PROPN
ma-207	188	2	]	]	PUNCT
ma-207	188	3	≤	≤	NUM
ma-207	188	4	1	1	NUM
ma-207	188	5	λ	λ	NOUN
ma-207	188	6	[	[	X
ma-207	188	7	∫	∫	PROPN
ma-207	188	8	1	1	NUM
ma-207	188	9	0	0	NUM
ma-207	188	10	w0((1−	w0((1−	NOUN
ma-207	188	11	θ)ρ)dθ	θ)ρ)dθ	PART
ma-207	188	12	+	+	CCONJ
ma-207	188	13	w0(ρ	w0(ρ	NOUN
ma-207	188	14	)	)	PUNCT
ma-207	189	1	+	+	CCONJ
ma-207	189	2	∫	∫	PROPN
ma-207	189	3	1	1	NUM
ma-207	189	4	0	0	NUM
ma-207	189	5	w((1−	w((1−	NUM
ma-207	189	6	θ)ρ)dθ	θ)ρ)dθ	X
ma-207	189	7	+	+	CCONJ
ma-207	189	8	w1(ρ	w1(ρ	NOUN
ma-207	189	9	)	)	PUNCT
ma-207	189	10	]	]	PUNCT
ma-207	190	1	ρ	ρ	X
ma-207	190	2	≤	≤	NUM
ma-207	190	3	β	β	X
ma-207	190	4	.	.	PUNCT
ma-207	191	1	notice	notice	VERB
ma-207	191	2	that	that	SCONJ
ma-207	191	3	xm	xm	PROPN
ma-207	191	4	∈	∈	PROPN
ma-207	191	5	q−1[f	q−1[f	PUNCT
ma-207	191	6	(	(	PUNCT
ma-207	191	7	x0	x0	PROPN
ma-207	191	8	)	)	PUNCT
ma-207	192	1	+	+	NOUN
ma-207	192	2	m(xm	m(xm	NOUN
ma-207	192	3	−	−	NOUN
ma-207	193	1	x0)−	x0)−	X
ma-207	193	2	f	f	PROPN
ma-207	193	3	(	(	PUNCT
ma-207	193	4	xm−1	xm−1	PROPN
ma-207	193	5	−	−	PROPN
ma-207	193	6	l(xm−1(xm	l(xm−1(xm	PROPN
ma-207	193	7	−	−	PROPN
ma-207	193	8	xm−1)].by	xm−1)].by	PROPN
ma-207	194	1	aubin	aubin	PROPN
ma-207	194	2	property	property	NOUN
ma-207	194	3	of	of	ADP
ma-207	194	4	q−1	q−1	PROPN
ma-207	194	5	(	(	PUNCT
ma-207	194	6	.	.	PUNCT
ma-207	194	7	)	)	PUNCT
ma-207	195	1	at	at	ADP
ma-207	195	2	(	(	PUNCT
ma-207	195	3	0	0	NUM
ma-207	195	4	,	,	PUNCT
ma-207	195	5	x1	x1	NUM
ma-207	195	6	)	)	PUNCT
ma-207	195	7	with	with	ADP
ma-207	195	8	modulus	modulus	ADJ
ma-207	195	9	λ	λ	PROPN
ma-207	195	10	and	and	CCONJ
ma-207	195	11	parameters	parameter	NOUN
ma-207	195	12	α	α	X
ma-207	195	13	,	,	PUNCT
ma-207	195	14	β	β	X
ma-207	195	15	we	we	PRON
ma-207	195	16	have	have	VERB
ma-207	195	17	in	in	ADP
ma-207	195	18	turn	turn	NOUN
ma-207	195	19	https://doi.org/10.28924/ada/ma.4.3	https://doi.org/10.28924/ada/ma.4.3	PROPN
ma-207	195	20	eur	eur	PROPN
ma-207	195	21	.	.	PUNCT
ma-207	196	1	j.	j.	PROPN
ma-207	196	2	math	math	PROPN
ma-207	196	3	.	.	PUNCT
ma-207	197	1	anal	anal	PROPN
ma-207	197	2	.	.	PUNCT
ma-207	198	1	10.28924	10.28924	NUM
ma-207	198	2	/	/	SYM
ma-207	198	3	ada	ada	PROPN
ma-207	198	4	/	/	SYM
ma-207	198	5	ma.4.3	ma.4.3	PROPN
ma-207	198	6	7	7	NUM
ma-207	198	7	d(xm	d(xm	PROPN
ma-207	198	8	,	,	PUNCT
ma-207	198	9	ψm(xm	ψm(xm	PROPN
ma-207	198	10	)	)	PUNCT
ma-207	198	11	)	)	PUNCT
ma-207	199	1	≤	≤	NUM
ma-207	199	2	e{q−1[f	e{q−1[f	ADV
ma-207	199	3	(	(	PUNCT
ma-207	199	4	x0	x0	PROPN
ma-207	199	5	)	)	PUNCT
ma-207	200	1	+	+	NOUN
ma-207	200	2	m(xm	m(xm	NOUN
ma-207	200	3	−	−	PROPN
ma-207	200	4	x0)−	x0)−	PROPN
ma-207	200	5	f	f	PROPN
ma-207	200	6	(	(	PUNCT
ma-207	200	7	xm−1)−	xm−1)−	PROPN
ma-207	200	8	l(xm−1)(xm	l(xm−1)(xm	PROPN
ma-207	201	1	−	−	PROPN
ma-207	201	2	xm−1	xm−1	PROPN
ma-207	201	3	)	)	PUNCT
ma-207	201	4	]	]	PUNCT
ma-207	202	1	∩s(x1	∩s(x1	ADJ
ma-207	202	2	,	,	PUNCT
ma-207	202	3	α	α	NOUN
ma-207	202	4	)	)	PUNCT
ma-207	202	5	,	,	PUNCT
ma-207	202	6	ψm(xm	ψm(xm	PROPN
ma-207	202	7	)	)	PUNCT
ma-207	202	8	}	}	PUNCT
ma-207	202	9	≤	≤	NUM
ma-207	202	10	λ‖f	λ‖f	NOUN
ma-207	202	11	(	(	PUNCT
ma-207	202	12	xm)−	xm)−	PROPN
ma-207	202	13	f	f	PROPN
ma-207	203	1	(	(	PUNCT
ma-207	203	2	xm−1)−	xm−1)−	PROPN
ma-207	203	3	l(xm−1)(xm	l(xm−1)(xm	PROPN
ma-207	204	1	−	−	PROPN
ma-207	204	2	xm−1)‖	xm−1)‖	NOUN
ma-207	204	3	≤	≤	X
ma-207	204	4	λ‖f	λ‖f	CCONJ
ma-207	204	5	(	(	PUNCT
ma-207	204	6	xm)−	xm)−	PROPN
ma-207	204	7	f	f	PROPN
ma-207	205	1	(	(	PUNCT
ma-207	205	2	xm−1)−	xm−1)−	PROPN
ma-207	205	3	f	f	PROPN
ma-207	205	4	′(xm−1)(xm	′(xm−1)(xm	VERB
ma-207	205	5	−	−	PROPN
ma-207	205	6	xm−1)‖	xm−1)‖	PUNCT
ma-207	206	1	+	+	PROPN
ma-207	206	2	λ‖(l(xm−1)−	λ‖(l(xm−1)−	PROPN
ma-207	206	3	f	f	PROPN
ma-207	206	4	′(xm−1))(xm	′(xm−1))(xm	PROPN
ma-207	206	5	−	−	PROPN
ma-207	206	6	xm−1)‖	xm−1)‖	PROPN
ma-207	207	1	≤	≤	X
ma-207	207	2	λ‖f	λ‖f	CCONJ
ma-207	207	3	(	(	PUNCT
ma-207	207	4	xm)−	xm)−	PROPN
ma-207	207	5	f	f	PROPN
ma-207	207	6	(	(	PUNCT
ma-207	207	7	xm−1)−	xm−1)−	PROPN
ma-207	207	8	f	f	PROPN
ma-207	207	9	′(xm−1)(xm	′(xm−1)(xm	VERB
ma-207	207	10	−	−	PROPN
ma-207	207	11	xm−1)‖	xm−1)‖	PUNCT
ma-207	208	1	+	+	PUNCT
ma-207	208	2	λ‖(l(xm−1)−m)(xm	λ‖(l(xm−1)−m)(xm	NUM
ma-207	208	3	−	−	NOUN
ma-207	208	4	xm−1)‖	xm−1)‖	PUNCT
ma-207	209	1	+	+	PROPN
ma-207	209	2	λ‖(f	λ‖(f	PROPN
ma-207	209	3	′(xm−1)−m)(xm	′(xm−1)−m)(xm	PROPN
ma-207	209	4	−	−	PROPN
ma-207	210	1	xm−1)‖	xm−1)‖	PROPN
ma-207	210	2	≤	≤	PROPN
ma-207	211	1	[	[	X
ma-207	211	2	∫	∫	PROPN
ma-207	211	3	1	1	NUM
ma-207	211	4	0	0	NUM
ma-207	211	5	w((1−	w((1−	PROPN
ma-207	211	6	θ)‖xm	θ)‖xm	X
ma-207	211	7	−	−	NOUN
ma-207	211	8	xm−1‖)dθ‖xm	xm−1‖)dθ‖xm	PUNCT
ma-207	212	1	−	−	PROPN
ma-207	212	2	xm−1‖	xm−1‖	PROPN
ma-207	213	1	+	+	CCONJ
ma-207	213	2	w0(‖xm−1	w0(‖xm−1	PROPN
ma-207	213	3	−	−	PROPN
ma-207	213	4	x0‖)‖xm	x0‖)‖xm	PUNCT
ma-207	214	1	−	−	NOUN
ma-207	214	2	xm−1‖+	xm−1‖+	NOUN
ma-207	214	3	w1(‖xm−1	w1(‖xm−1	PROPN
ma-207	214	4	−	−	PROPN
ma-207	214	5	x0‖)‖xm	x0‖)‖xm	PROPN
ma-207	215	1	−	−	PROPN
ma-207	215	2	xm−1‖	xm−1‖	PROPN
ma-207	215	3	]	]	X
ma-207	215	4	=	=	PUNCT
ma-207	215	5	γ(1−	γ(1−	PROPN
ma-207	215	6	w0(‖xm	w0(‖xm	PROPN
ma-207	215	7	−	−	PROPN
ma-207	215	8	x0‖	x0‖	PROPN
ma-207	215	9	)	)	PUNCT
ma-207	215	10	)	)	PUNCT
ma-207	215	11	,	,	PUNCT
ma-207	215	12	where	where	SCONJ
ma-207	215	13	γ	γ	X
ma-207	215	14	=	=	PUNCT
ma-207	216	1	[	[	X
ma-207	216	2	∫	∫	PROPN
ma-207	216	3	1	1	NUM
ma-207	216	4	0	0	NUM
ma-207	216	5	w((1−	w((1−	PROPN
ma-207	216	6	θ)‖xm	θ)‖xm	NUM
ma-207	216	7	−	−	NUM
ma-207	216	8	xm−1‖)dθ	xm−1‖)dθ	NOUN
ma-207	216	9	+	+	CCONJ
ma-207	216	10	w0(‖xm−1	w0(‖xm−1	PROPN
ma-207	216	11	−	−	PROPN
ma-207	216	12	x0‖	x0‖	PROPN
ma-207	216	13	)	)	PUNCT
ma-207	217	1	+	+	CCONJ
ma-207	217	2	w1(‖xm−1	w1(‖xm−1	PROPN
ma-207	217	3	−	−	PROPN
ma-207	217	4	x0‖	x0‖	PROPN
ma-207	217	5	)	)	PUNCT
ma-207	217	6	]	]	PUNCT
ma-207	217	7	1−	1−	NUM
ma-207	218	1	w0(‖xm	w0(‖xm	PRON
ma-207	218	2	−	−	PROPN
ma-207	218	3	x0‖	x0‖	PROPN
ma-207	218	4	)	)	PUNCT
ma-207	218	5	×‖xm	×‖xm	PUNCT
ma-207	218	6	−	−	PROPN
ma-207	218	7	xm−1‖	xm−1‖	PROPN
ma-207	218	8	(	(	PUNCT
ma-207	218	9	3.4	3.4	NUM
ma-207	218	10	)	)	PUNCT
ma-207	218	11	pick	pick	NOUN
ma-207	218	12	v1	v1	NOUN
ma-207	218	13	,	,	PUNCT
ma-207	218	14	v2	v2	PROPN
ma-207	218	15	∈	∈	PROPN
ma-207	218	16	s(xm	s(xm	NOUN
ma-207	218	17	,	,	PUNCT
ma-207	218	18	‖xm	‖xm	PROPN
ma-207	218	19	−	−	PROPN
ma-207	218	20	x0‖	x0‖	PROPN
ma-207	218	21	)	)	PUNCT
ma-207	218	22	.	.	PUNCT
ma-207	219	1	then	then	ADV
ma-207	219	2	,	,	PUNCT
ma-207	219	3	we	we	PRON
ma-207	219	4	get	get	VERB
ma-207	219	5	e{ψm(v1	e{ψm(v1	NOUN
ma-207	219	6	)	)	PUNCT
ma-207	219	7	∩	∩	PROPN
ma-207	219	8	s(xm	s(xm	PROPN
ma-207	219	9	,	,	PUNCT
ma-207	219	10	‖xm	‖xm	PROPN
ma-207	219	11	−	−	PROPN
ma-207	219	12	x0‖	x0‖	PROPN
ma-207	219	13	)	)	PUNCT
ma-207	219	14	,	,	PUNCT
ma-207	219	15	ψm(v2	ψm(v2	NOUN
ma-207	219	16	)	)	PUNCT
ma-207	219	17	}	}	PUNCT
ma-207	219	18	≤	≤	NUM
ma-207	219	19	e{ψm(v1	e{ψm(v1	PROPN
ma-207	219	20	)	)	PUNCT
ma-207	219	21	∩	∩	ADJ
ma-207	219	22	s(x1	s(x1	NOUN
ma-207	219	23	,	,	PUNCT
ma-207	219	24	α	α	NOUN
ma-207	219	25	)	)	PUNCT
ma-207	219	26	,	,	PUNCT
ma-207	219	27	ψm(v2	ψm(v2	NOUN
ma-207	219	28	)	)	PUNCT
ma-207	219	29	}	}	PUNCT
ma-207	219	30	≤	≤	NUM
ma-207	219	31	λ‖m	λ‖m	NOUN
ma-207	220	1	−	−	PROPN
ma-207	220	2	l(xm)‖‖v1	l(xm)‖‖v1	PROPN
ma-207	220	3	−	−	PROPN
ma-207	220	4	v2‖	v2‖	PROPN
ma-207	220	5	≤	≤	NOUN
ma-207	220	6	w0(‖xm	w0(‖xm	PROPN
ma-207	220	7	−	−	PROPN
ma-207	220	8	x0‖)‖v1	x0‖)‖v1	PROPN
ma-207	220	9	−	−	PROPN
ma-207	220	10	v2‖	v2‖	PROPN
ma-207	220	11	≤	≤	PROPN
ma-207	220	12	w0(ρ)‖v1	w0(ρ)‖v1	VERB
ma-207	220	13	−	−	PROPN
ma-207	220	14	v2‖	v2‖	PROPN
ma-207	220	15	,	,	PUNCT
ma-207	220	16	where	where	SCONJ
ma-207	220	17	w0(ρ	w0(ρ	NOUN
ma-207	220	18	)	)	PUNCT
ma-207	220	19	<	<	X
ma-207	220	20	1	1	NUM
ma-207	220	21	,	,	PUNCT
ma-207	220	22	by	by	ADP
ma-207	220	23	the	the	DET
ma-207	220	24	definition	definition	NOUN
ma-207	220	25	of	of	ADP
ma-207	220	26	ρ	ρ	PROPN
ma-207	220	27	.	.	PUNCT
ma-207	221	1	thus	thus	ADV
ma-207	221	2	,	,	PUNCT
ma-207	221	3	the	the	DET
ma-207	221	4	theorem	theorem	NOUN
ma-207	221	5	2.2	2.2	NUM
ma-207	221	6	is	be	AUX
ma-207	221	7	applicable	applicable	ADJ
ma-207	221	8	if	if	SCONJ
ma-207	221	9	we	we	PRON
ma-207	221	10	take	take	VERB
ma-207	221	11	ψ	ψ	X
ma-207	221	12	=	=	SYM
ma-207	221	13	ψm	ψm	PROPN
ma-207	221	14	,	,	PUNCT
ma-207	221	15	γ0	γ0	NOUN
ma-207	221	16	=	=	PUNCT
ma-207	221	17	γ	γ	NOUN
ma-207	221	18	and	and	CCONJ
ma-207	221	19	δ0	δ0	NOUN
ma-207	221	20	=	=	SYM
ma-207	221	21	δ	δ	PROPN
ma-207	221	22	=	=	PUNCT
ma-207	222	1	w0(‖xm	w0(‖xm	PROPN
ma-207	222	2	−	−	NOUN
ma-207	222	3	x0‖	x0‖	PROPN
ma-207	222	4	)	)	PUNCT
ma-207	222	5	.	.	PUNCT
ma-207	223	1	so	so	ADV
ma-207	223	2	,	,	PUNCT
ma-207	223	3	there	there	PRON
ma-207	223	4	exists	exist	VERB
ma-207	223	5	xm+1	xm+1	PROPN
ma-207	223	6	∈	∈	PROPN
ma-207	223	7	s[x∗	s[x∗	PROPN
ma-207	223	8	,	,	PUNCT
ma-207	223	9	ρ	ρ	NOUN
ma-207	223	10	]	]	PUNCT
ma-207	223	11	satisfying	satisfy	VERB
ma-207	223	12	xm+1	xm+1	PROPN
ma-207	223	13	∈	∈	PROPN
ma-207	223	14	q−1[f	q−1[f	PUNCT
ma-207	223	15	(	(	PUNCT
ma-207	223	16	x0	x0	PROPN
ma-207	223	17	)	)	PUNCT
ma-207	224	1	+	+	NOUN
ma-207	224	2	m(xm+1	m(xm+1	PROPN
ma-207	224	3	−	−	PROPN
ma-207	224	4	x0)−	x0)−	X
ma-207	224	5	f	f	PROPN
ma-207	224	6	(	(	PUNCT
ma-207	224	7	xm)−	xm)−	PROPN
ma-207	224	8	l(xm)(xm+1	l(xm)(xm+1	PROPN
ma-207	224	9	−	−	PROPN
ma-207	224	10	xm	xm	PROPN
ma-207	224	11	)	)	PUNCT
ma-207	224	12	]	]	PUNCT
ma-207	224	13	leading	lead	VERB
ma-207	224	14	to	to	ADP
ma-207	224	15	‖xm+1	‖xm+1	PROPN
ma-207	224	16	−	−	PROPN
ma-207	224	17	xm‖	xm‖	PROPN
ma-207	224	18	≤	≤	PROPN
ma-207	224	19	[	[	X
ma-207	224	20	∫	∫	PROPN
ma-207	224	21	1	1	NUM
ma-207	224	22	0	0	NUM
ma-207	224	23	w((1−	w((1−	NUM
ma-207	224	24	θ)(sm	θ)(sm	NOUN
ma-207	224	25	−	−	NOUN
ma-207	224	26	sm−1))dθ	sm−1))dθ	PROPN
ma-207	224	27	+	+	CCONJ
ma-207	224	28	w0(‖sm−1‖	w0(‖sm−1‖	PROPN
ma-207	224	29	)	)	PUNCT
ma-207	224	30	+	+	NUM
ma-207	224	31	w1(sm−1	w1(sm−1	NOUN
ma-207	224	32	)	)	PUNCT
ma-207	224	33	]	]	PUNCT
ma-207	224	34	1−	1−	NUM
ma-207	224	35	w0(sm	w0(sm	NUM
ma-207	224	36	)	)	PUNCT
ma-207	224	37	×(sm	×(sm	VERB
ma-207	224	38	−	−	PROPN
ma-207	224	39	sm−1	sm−1	NOUN
ma-207	224	40	)	)	PUNCT
ma-207	224	41	(	(	PUNCT
ma-207	224	42	3.5	3.5	NUM
ma-207	224	43	)	)	PUNCT
ma-207	224	44	≤	≤	NOUN
ma-207	224	45	sm+1	sm+1	PROPN
ma-207	225	1	−	−	PROPN
ma-207	225	2	sm	sm	PROPN
ma-207	225	3	,	,	PUNCT
ma-207	225	4	https://doi.org/10.28924/ada/ma.4.3	https://doi.org/10.28924/ada/ma.4.3	PROPN
ma-207	225	5	eur	eur	PROPN
ma-207	225	6	.	.	PUNCT
ma-207	226	1	j.	j.	PROPN
ma-207	226	2	math	math	PROPN
ma-207	226	3	.	.	PUNCT
ma-207	227	1	anal	anal	PROPN
ma-207	227	2	.	.	PUNCT
ma-207	228	1	10.28924	10.28924	NUM
ma-207	228	2	/	/	SYM
ma-207	228	3	ada	ada	PROPN
ma-207	228	4	/	/	SYM
ma-207	228	5	ma.4.3	ma.4.3	PROPN
ma-207	228	6	8where	8where	NUM
ma-207	228	7	we	we	PRON
ma-207	228	8	used	use	VERB
ma-207	228	9	(	(	PUNCT
ma-207	228	10	a2	a2	PROPN
ma-207	228	11	)	)	PUNCT
ma-207	228	12	,	,	PUNCT
ma-207	228	13	(	(	PUNCT
ma-207	228	14	3.4	3.4	NUM
ma-207	228	15	)	)	PUNCT
ma-207	228	16	and	and	CCONJ
ma-207	228	17	the	the	DET
ma-207	228	18	induction	induction	NOUN
ma-207	228	19	hypothesis	hypothesis	NOUN
ma-207	228	20	(	(	PUNCT
ma-207	228	21	3.3).by	3.3).by	NUM
ma-207	228	22	(	(	PUNCT
ma-207	228	23	a3	a3	NOUN
ma-207	228	24	)	)	PUNCT
ma-207	228	25	and	and	CCONJ
ma-207	228	26	(	(	PUNCT
ma-207	228	27	3.5	3.5	NUM
ma-207	228	28	)	)	PUNCT
ma-207	228	29	,	,	PUNCT
ma-207	228	30	we	we	PRON
ma-207	228	31	obtain	obtain	VERB
ma-207	228	32	∞∑	∞∑	NUM
ma-207	228	33	m	m	NOUN
ma-207	228	34	=	=	NOUN
ma-207	228	35	m0	m0	X
ma-207	228	36	‖xm+1	‖xm+1	PUNCT
ma-207	228	37	−	−	PROPN
ma-207	228	38	xm‖	xm‖	PROPN
ma-207	228	39	≤	≤	NOUN
ma-207	229	1	∞∑	∞∑	NUM
ma-207	229	2	m	m	NOUN
ma-207	229	3	=	=	NOUN
ma-207	229	4	m0	m0	X
ma-207	229	5	(	(	PUNCT
ma-207	229	6	sm+1	sm+1	CCONJ
ma-207	229	7	−	−	PROPN
ma-207	229	8	sm	sm	PROPN
ma-207	229	9	)	)	PUNCT
ma-207	229	10	≤	≤	PROPN
ma-207	229	11	s	s	AUX
ma-207	229	12	−	−	NOUN
ma-207	229	13	sm0	sm0	NOUN
ma-207	229	14	<	<	X
ma-207	230	1	+	+	NOUN
ma-207	230	2	∞.	∞.	PROPN
ma-207	230	3	if	if	SCONJ
ma-207	230	4	follows	follow	VERB
ma-207	230	5	that	that	SCONJ
ma-207	230	6	the	the	DET
ma-207	230	7	sequence	sequence	NOUN
ma-207	230	8	{	{	PUNCT
ma-207	230	9	xm	xm	NOUN
ma-207	230	10	}	}	PUNCT
ma-207	230	11	is	be	AUX
ma-207	230	12	complete	complete	ADJ
ma-207	230	13	in	in	ADP
ma-207	230	14	a	a	DET
ma-207	230	15	banach	banach	NOUN
ma-207	230	16	space	space	NOUN
ma-207	230	17	b1	b1	NOUN
ma-207	230	18	,	,	PUNCT
ma-207	230	19	and	and	CCONJ
ma-207	230	20	as	as	ADP
ma-207	230	21	such	such	ADJ
ma-207	230	22	it	it	PRON
ma-207	230	23	is	be	AUX
ma-207	230	24	convergentto	convergentto	ADJ
ma-207	230	25	some	some	DET
ma-207	230	26	x∗	x∗	PROPN
ma-207	230	27	∈	∈	PROPN
ma-207	230	28	s[x0	s[x0	NOUN
ma-207	230	29	,	,	PUNCT
ma-207	230	30	s	s	NOUN
ma-207	230	31	]	]	X
ma-207	230	32	.	.	PUNCT
ma-207	231	1	then	then	ADV
ma-207	231	2	,	,	PUNCT
ma-207	231	3	by	by	ADP
ma-207	231	4	(	(	PUNCT
ma-207	231	5	3.3	3.3	NUM
ma-207	231	6	)	)	PUNCT
ma-207	231	7	,	,	PUNCT
ma-207	231	8	we	we	PRON
ma-207	231	9	can	can	AUX
ma-207	231	10	write	write	VERB
ma-207	231	11	‖xm+j	‖xm+j	PROPN
ma-207	231	12	−	−	PROPN
ma-207	231	13	xn‖	xn‖	PROPN
ma-207	231	14	≤	≤	PROPN
ma-207	231	15	‖xm+j	‖xm+j	PROPN
ma-207	231	16	−	−	PROPN
ma-207	231	17	xm+j−1‖+	xm+j−1‖+	NOUN
ma-207	231	18	‖xm+j−1	‖xm+j−1	PRON
ma-207	231	19	−	−	PROPN
ma-207	231	20	xm+j−2‖+	xm+j−2‖+	NUM
ma-207	231	21	‖xm+1	‖xm+1	NUM
ma-207	232	1	−	−	PROPN
ma-207	232	2	xn‖	xn‖	PROPN
ma-207	232	3	≤	≤	ADJ
ma-207	232	4	sm+j	sm+j	NUM
ma-207	232	5	−	−	NOUN
ma-207	233	1	sm+j−1	sm+j−1	NOUN
ma-207	234	1	+	+	CCONJ
ma-207	235	1	sm+j−1	sm+j−1	NOUN
ma-207	235	2	−	−	PROPN
ma-207	235	3	sm+j−2	sm+j−2	PROPN
ma-207	235	4	+	+	CCONJ
ma-207	235	5	...	...	PUNCT
ma-207	236	1	+	+	CCONJ
ma-207	236	2	sm+1	sm+1	NUM
ma-207	236	3	−	−	PROPN
ma-207	236	4	sn	sn	NOUN
ma-207	236	5	=	=	SYM
ma-207	236	6	sm+j	sm+j	PROPN
ma-207	236	7	−	−	NOUN
ma-207	237	1	sm	sm	INTJ
ma-207	237	2	.	.	PUNCT
ma-207	237	3	(	(	PUNCT
ma-207	237	4	3.6	3.6	NUM
ma-207	237	5	)	)	PUNCT
ma-207	237	6	by	by	ADP
ma-207	237	7	letting	let	VERB
ma-207	237	8	j	j	PROPN
ma-207	237	9	−→	−→	NOUN
ma-207	237	10	+	+	NOUN
ma-207	237	11	∞	∞	PROPN
ma-207	237	12	in	in	ADP
ma-207	237	13	(	(	PUNCT
ma-207	237	14	3.6	3.6	NUM
ma-207	237	15	)	)	PUNCT
ma-207	237	16	,	,	PUNCT
ma-207	237	17	we	we	PRON
ma-207	237	18	conclude	conclude	VERB
ma-207	237	19	that	that	SCONJ
ma-207	237	20	(	(	PUNCT
ma-207	237	21	3.2	3.2	NUM
ma-207	237	22	)	)	PUNCT
ma-207	237	23	is	be	AUX
ma-207	237	24	valid	valid	ADJ
ma-207	237	25	.	.	PUNCT
ma-207	238	1	in	in	ADP
ma-207	238	2	view	view	NOUN
ma-207	238	3	of	of	ADP
ma-207	238	4	the	the	DET
ma-207	238	5	definition	definition	NOUN
ma-207	238	6	the	the	DET
ma-207	238	7	sequence	sequence	NOUN
ma-207	238	8	{	{	PUNCT
ma-207	238	9	xm	xm	PROPN
ma-207	238	10	}	}	PUNCT
ma-207	238	11	,	,	PUNCT
ma-207	238	12	0	0	NUM
ma-207	238	13	∈	∈	PROPN
ma-207	238	14	f	f	X
ma-207	238	15	(	(	PUNCT
ma-207	238	16	xm	xm	PROPN
ma-207	238	17	)	)	PUNCT
ma-207	238	18	+	+	NOUN
ma-207	238	19	l(xm)(xm+1−xm	l(xm)(xm+1−xm	NOUN
ma-207	238	20	)	)	PUNCT
ma-207	238	21	+	+	NOUN
ma-207	238	22	g(xn+1	g(xn+1	NOUN
ma-207	238	23	)	)	PUNCT
ma-207	238	24	for	for	ADP
ma-207	238	25	each	each	DET
ma-207	238	26	m	m	PROPN
ma-207	238	27	=	=	SYM
ma-207	238	28	0	0	NUM
ma-207	238	29	,	,	PUNCT
ma-207	238	30	1	1	NUM
ma-207	238	31	,	,	PUNCT
ma-207	238	32	...	...	PUNCT
ma-207	238	33	then	then	ADV
ma-207	238	34	,	,	PUNCT
ma-207	238	35	by	by	ADP
ma-207	238	36	letting	let	VERB
ma-207	238	37	m	m	PRON
ma-207	238	38	−→	−→	ADJ
ma-207	239	1	+	+	ADV
ma-207	239	2	∞,we	∞,we	NUM
ma-207	239	3	deduce	deduce	VERB
ma-207	239	4	that	that	SCONJ
ma-207	239	5	0	0	NUM
ma-207	239	6	∈	∈	PROPN
ma-207	239	7	f	f	X
ma-207	239	8	(	(	PUNCT
ma-207	239	9	x∗	x∗	PROPN
ma-207	239	10	)	)	PUNCT
ma-207	239	11	+	+	CCONJ
ma-207	239	12	g(x∗	g(x∗	PRON
ma-207	239	13	)	)	PUNCT
ma-207	239	14	.	.	PUNCT
ma-207	240	1	�	�	PROPN
ma-207	240	2	remark	remark	VERB
ma-207	240	3	3.2	3.2	NUM
ma-207	240	4	.	.	PUNCT
ma-207	241	1	a	a	DET
ma-207	241	2	popular	popular	ADJ
ma-207	241	3	choice	choice	NOUN
ma-207	241	4	for	for	ADP
ma-207	241	5	m	m	PROPN
ma-207	241	6	=	=	SYM
ma-207	241	7	f	f	PROPN
ma-207	241	8	′(x0	′(x0	NOUN
ma-207	241	9	)	)	PUNCT
ma-207	241	10	.	.	PUNCT
ma-207	242	1	but	but	CCONJ
ma-207	242	2	this	this	PRON
ma-207	242	3	is	be	AUX
ma-207	242	4	not	not	PART
ma-207	242	5	necessarily	necessarily	ADV
ma-207	242	6	the	the	DET
ma-207	242	7	most	most	ADV
ma-207	242	8	flexible	flexible	ADJ
ma-207	242	9	choice	choice	NOUN
ma-207	242	10	.	.	PUNCT
ma-207	243	1	the	the	DET
ma-207	243	2	two	two	NUM
ma-207	243	3	conditions	condition	NOUN
ma-207	243	4	in	in	ADP
ma-207	243	5	(	(	PUNCT
ma-207	243	6	a3	a3	NOUN
ma-207	243	7	)	)	PUNCT
ma-207	243	8	are	be	AUX
ma-207	243	9	very	very	ADV
ma-207	243	10	general	general	ADJ
ma-207	243	11	.	.	PUNCT
ma-207	244	1	by	by	ADP
ma-207	244	2	specializing	specialize	VERB
ma-207	244	3	the	the	DET
ma-207	244	4	functions	function	NOUN
ma-207	244	5	w0	w0	PROPN
ma-207	244	6	,	,	PUNCT
ma-207	244	7	w	w	NOUN
ma-207	244	8	and	and	CCONJ
ma-207	244	9	w1	w1	NOUN
ma-207	244	10	,	,	PUNCT
ma-207	244	11	we	we	PRON
ma-207	244	12	can	can	AUX
ma-207	244	13	provide	provide	VERB
ma-207	244	14	other	other	ADJ
ma-207	244	15	stronger	strong	ADJ
ma-207	244	16	conditions	condition	NOUN
ma-207	244	17	that	that	PRON
ma-207	244	18	imply	imply	VERB
ma-207	244	19	the	the	DET
ma-207	244	20	ones	one	NOUN
ma-207	244	21	in	in	ADP
ma-207	244	22	(	(	PUNCT
ma-207	244	23	a3	a3	NOUN
ma-207	244	24	)	)	PUNCT
ma-207	244	25	.	.	PUNCT
ma-207	245	1	let	let	VERB
ma-207	245	2	us	we	PRON
ma-207	245	3	consider	consider	VERB
ma-207	245	4	the	the	DET
ma-207	245	5	interesting	interesting	ADJ
ma-207	245	6	lipchitz	lipchitz	NOUN
ma-207	245	7	case	case	NOUN
ma-207	245	8	,	,	PUNCT
ma-207	245	9	i.e.	i.e.	X
ma-207	245	10	when	when	SCONJ
ma-207	245	11	w0(t	w0(t	PROPN
ma-207	245	12	)	)	PUNCT
ma-207	245	13	=	=	SYM
ma-207	245	14	l0	l0	PROPN
ma-207	245	15	t	t	PROPN
ma-207	245	16	,	,	PUNCT
ma-207	245	17	w(t	w(t	PROPN
ma-207	245	18	)	)	PUNCT
ma-207	246	1	=	=	SYM
ma-207	246	2	l	l	NOUN
ma-207	246	3	t	t	NOUN
ma-207	246	4	and	and	CCONJ
ma-207	246	5	w1(t	w1(t	NUM
ma-207	246	6	)	)	PUNCT
ma-207	246	7	=	=	SYM
ma-207	246	8	l1	l1	PROPN
ma-207	246	9	t	t	PROPN
ma-207	246	10	.	.	PUNCT
ma-207	247	1	then	then	ADV
ma-207	247	2	,	,	PUNCT
ma-207	247	3	the	the	DET
ma-207	247	4	sequence	sequence	NOUN
ma-207	247	5	{	{	PUNCT
ma-207	247	6	sn	sn	NOUN
ma-207	247	7	}	}	PUNCT
ma-207	247	8	in	in	ADP
ma-207	247	9	(	(	PUNCT
ma-207	247	10	a2	a2	NOUN
ma-207	247	11	)	)	PUNCT
ma-207	247	12	reduces	reduce	VERB
ma-207	247	13	for	for	ADP
ma-207	247	14	l2	l2	NOUN
ma-207	247	15	=	=	SYM
ma-207	247	16	l0	l0	PROPN
ma-207	247	17	+	+	CCONJ
ma-207	247	18	l1	l1	PROPN
ma-207	247	19	to	to	ADP
ma-207	247	20	sn+1	sn+1	PROPN
ma-207	247	21	=	=	SYM
ma-207	247	22	sn	sn	PROPN
ma-207	248	1	+	+	CCONJ
ma-207	248	2	(	(	PUNCT
ma-207	248	3	l	l	NOUN
ma-207	248	4	2(sn	2(sn	NUM
ma-207	249	1	−	−	NOUN
ma-207	249	2	sn−1	sn−1	PROPN
ma-207	249	3	)	)	PUNCT
ma-207	250	1	+	+	CCONJ
ma-207	250	2	sn−1	sn−1	PROPN
ma-207	250	3	)	)	PUNCT
ma-207	250	4	(	(	PUNCT
ma-207	250	5	sn	sn	NOUN
ma-207	250	6	−	−	PROPN
ma-207	250	7	sn−1	sn−1	PROPN
ma-207	250	8	)	)	PUNCT
ma-207	250	9	1−	1−	NUM
ma-207	250	10	l0(sn	l0(sn	NUM
ma-207	250	11	)	)	PUNCT
ma-207	250	12	(	(	PUNCT
ma-207	250	13	3.7	3.7	NUM
ma-207	250	14	)	)	PUNCT
ma-207	250	15	such	such	ADJ
ma-207	250	16	sequences	sequence	NOUN
ma-207	250	17	appear	appear	VERB
ma-207	250	18	as	as	ADP
ma-207	250	19	majorant	majorant	NOUN
ma-207	250	20	of	of	ADP
ma-207	250	21	newton	newton	PROPN
ma-207	250	22	-	-	PUNCT
ma-207	250	23	like	like	ADJ
ma-207	250	24	methods	method	NOUN
ma-207	250	25	for	for	ADP
ma-207	250	26	solving	solve	VERB
ma-207	250	27	nonlinear	nonlinear	ADJ
ma-207	250	28	equations	equation	NOUN
ma-207	250	29	(	(	PUNCT
ma-207	250	30	i.e.when	i.e.when	NOUN
ma-207	250	31	g	g	NOUN
ma-207	250	32	=	=	SYM
ma-207	250	33	{	{	PUNCT
ma-207	250	34	0	0	NUM
ma-207	250	35	}	}	PUNCT
ma-207	250	36	)	)	PUNCT
ma-207	250	37	.	.	PUNCT
ma-207	251	1	the	the	DET
ma-207	251	2	kantorovich	kantorovich	NOUN
ma-207	251	3	-	-	PUNCT
ma-207	251	4	type	type	NOUN
ma-207	251	5	convergence	convergence	NOUN
ma-207	251	6	conditions	condition	NOUN
ma-207	251	7	in	in	ADP
ma-207	251	8	such	such	ADJ
ma-207	251	9	studies	study	NOUN
ma-207	251	10	imply	imply	VERB
ma-207	251	11	the	the	DET
ma-207	251	12	ones	one	NOUN
ma-207	251	13	in	in	ADP
ma-207	251	14	(	(	PUNCT
ma-207	251	15	a3	a3	NOUN
ma-207	251	16	)	)	PUNCT
ma-207	251	17	but	but	CCONJ
ma-207	251	18	not	not	PART
ma-207	251	19	necessarily	necessarily	ADV
ma-207	251	20	vice	vice	ADV
ma-207	251	21	versa	versa	ADV
ma-207	252	1	[	[	X
ma-207	252	2	20,35	20,35	NOUN
ma-207	252	3	]	]	X
ma-207	252	4	.	.	PUNCT
ma-207	253	1	our	our	PRON
ma-207	253	2	approach	approach	NOUN
ma-207	253	3	for	for	ADP
ma-207	253	4	the	the	DET
ma-207	253	5	study	study	NOUN
ma-207	253	6	of	of	ADP
ma-207	253	7	majorizing	majorize	VERB
ma-207	253	8	sequence	sequence	NOUN
ma-207	253	9	{	{	PUNCT
ma-207	253	10	sn}has	sn}has	PUNCT
ma-207	253	11	provided	provide	VERB
ma-207	253	12	even	even	ADV
ma-207	253	13	weaker	weak	ADJ
ma-207	253	14	convergence	convergence	NOUN
ma-207	253	15	conditions	condition	NOUN
ma-207	253	16	than	than	ADP
ma-207	253	17	the	the	DET
ma-207	253	18	kantorovich	kantorovich	NOUN
ma-207	253	19	-	-	PUNCT
ma-207	253	20	type	type	NOUN
ma-207	253	21	[	[	X
ma-207	253	22	4,5,6	4,5,6	NUM
ma-207	253	23	]	]	NOUN
ma-207	253	24	.	.	PUNCT
ma-207	253	25	4	4	X
ma-207	253	26	.	.	X
ma-207	253	27	conclusion	conclusion	NOUN
ma-207	253	28	a	a	DET
ma-207	253	29	very	very	ADV
ma-207	253	30	general	general	ADJ
ma-207	253	31	theory	theory	NOUN
ma-207	253	32	for	for	ADP
ma-207	253	33	studying	study	VERB
ma-207	253	34	the	the	DET
ma-207	253	35	convergence	convergence	NOUN
ma-207	253	36	of	of	ADP
ma-207	253	37	newton	newton	PROPN
ma-207	253	38	-	-	PUNCT
ma-207	253	39	like	like	ADJ
ma-207	253	40	methods	method	NOUN
ma-207	253	41	is	be	AUX
ma-207	253	42	developed	develop	VERB
ma-207	253	43	forgenerating	forgenerate	VERB
ma-207	253	44	sequences	sequence	NOUN
ma-207	253	45	approximating	approximate	VERB
ma-207	253	46	a	a	DET
ma-207	253	47	solution	solution	NOUN
ma-207	253	48	of	of	ADP
ma-207	253	49	a	a	DET
ma-207	253	50	generalized	generalized	ADJ
ma-207	253	51	equation	equation	NOUN
ma-207	253	52	involving	involve	VERB
ma-207	253	53	set	set	NOUN
ma-207	253	54	-	-	PUNCT
ma-207	253	55	valued	value	VERB
ma-207	253	56	op	op	NOUN
ma-207	253	57	-	-	PUNCT
ma-207	253	58	erators	erator	NOUN
ma-207	253	59	.	.	PUNCT
ma-207	254	1	the	the	DET
ma-207	254	2	semi	semi	ADJ
ma-207	254	3	-	-	ADJ
ma-207	254	4	local	local	ADJ
ma-207	254	5	analysis	analysis	NOUN
ma-207	254	6	of	of	ADP
ma-207	254	7	convergence	convergence	NOUN
ma-207	254	8	depend	depend	VERB
ma-207	254	9	on	on	ADP
ma-207	254	10	the	the	DET
ma-207	254	11	aubin	aubin	PROPN
ma-207	254	12	property	property	NOUN
ma-207	254	13	and	and	CCONJ
ma-207	254	14	the	the	DET
ma-207	254	15	conceptof	conceptof	NOUN
ma-207	254	16	generalized	generalize	VERB
ma-207	254	17	continuity	continuity	NOUN
ma-207	254	18	.	.	PUNCT
ma-207	255	1	the	the	DET
ma-207	255	2	error	error	NOUN
ma-207	255	3	analysis	analysis	NOUN
ma-207	255	4	includes	include	VERB
ma-207	255	5	,	,	PUNCT
ma-207	255	6	computable	computable	ADJ
ma-207	255	7	upper	upper	ADJ
ma-207	255	8	error	error	NOUN
ma-207	255	9	bounds	bound	NOUN
ma-207	255	10	on	on	ADP
ma-207	255	11	thenorms	thenorm	NOUN
ma-207	255	12	‖xn+1	‖xn+1	NUM
ma-207	255	13	−	−	NOUN
ma-207	255	14	xn‖	xn‖	PROPN
ma-207	255	15	and	and	CCONJ
ma-207	255	16	‖x∗	‖x∗	PUNCT
ma-207	256	1	−	−	PROPN
ma-207	257	1	xn‖.	xn‖.	PROPN
ma-207	257	2	in	in	ADP
ma-207	257	3	particular	particular	ADJ
ma-207	257	4	,	,	PUNCT
ma-207	257	5	the	the	DET
ma-207	257	6	semi	semi	ADJ
ma-207	257	7	-	-	ADJ
ma-207	257	8	local	local	ADJ
ma-207	257	9	analysis	analysis	NOUN
ma-207	257	10	of	of	ADP
ma-207	257	11	convergence	convergence	NOUN
ma-207	257	12	is	be	AUX
ma-207	257	13	basedon	basedon	NOUN
ma-207	257	14	majorizing	majorize	VERB
ma-207	257	15	sequences	sequence	NOUN
ma-207	257	16	for	for	ADP
ma-207	257	17	{	{	PUNCT
ma-207	257	18	xn	xn	PROPN
ma-207	257	19	}	}	PUNCT
ma-207	257	20	generated	generate	VERB
ma-207	257	21	by	by	ADP
ma-207	257	22	nlm	nlm	PROPN
ma-207	257	23	.	.	PUNCT
ma-207	258	1	it	it	PRON
ma-207	258	2	is	be	AUX
ma-207	258	3	shown	show	VERB
ma-207	258	4	that	that	SCONJ
ma-207	258	5	even	even	ADV
ma-207	258	6	specializations	specialization	NOUN
ma-207	258	7	of	of	ADP
ma-207	258	8	theoperators	theoperator	NOUN
ma-207	258	9	involved	involve	VERB
ma-207	258	10	lead	lead	VERB
ma-207	258	11	to	to	ADP
ma-207	258	12	better	well	ADJ
ma-207	258	13	results	result	NOUN
ma-207	258	14	when	when	SCONJ
ma-207	258	15	compared	compare	VERB
ma-207	258	16	to	to	ADP
ma-207	258	17	existing	exist	VERB
ma-207	258	18	ones	one	NOUN
ma-207	258	19	(	(	PUNCT
ma-207	258	20	see	see	VERB
ma-207	258	21	remark	remark	NOUN
ma-207	258	22	3.2	3.2	NUM
ma-207	258	23	)	)	PUNCT
ma-207	258	24	.	.	PUNCT
ma-207	259	1	the	the	DET
ma-207	259	2	https://doi.org/10.28924/ada/ma.4.3	https://doi.org/10.28924/ada/ma.4.3	PROPN
ma-207	259	3	eur	eur	PROPN
ma-207	259	4	.	.	PUNCT
ma-207	260	1	j.	j.	PROPN
ma-207	260	2	math	math	PROPN
ma-207	260	3	.	.	PUNCT
ma-207	261	1	anal	anal	PROPN
ma-207	261	2	.	.	PUNCT
ma-207	262	1	10.28924	10.28924	NUM
ma-207	262	2	/	/	SYM
ma-207	262	3	ada	ada	PROPN
ma-207	262	4	/	/	SYM
ma-207	262	5	ma.4.3	ma.4.3	PROPN
ma-207	262	6	9future	9future	NUM
ma-207	262	7	direction	direction	NOUN
ma-207	262	8	of	of	ADP
ma-207	262	9	our	our	PRON
ma-207	262	10	research	research	NOUN
ma-207	262	11	involves	involve	VERB
ma-207	262	12	the	the	DET
ma-207	262	13	application	application	NOUN
ma-207	262	14	of	of	ADP
ma-207	262	15	the	the	DET
ma-207	262	16	developed	develop	VERB
ma-207	262	17	theory	theory	NOUN
ma-207	262	18	on	on	ADP
ma-207	262	19	other	other	ADJ
ma-207	262	20	meth	meth	NOUN
ma-207	262	21	-	-	PUNCT
ma-207	262	22	ods	od	NOUN
ma-207	262	23	[	[	X
ma-207	262	24	1–3,9	1–3,9	NUM
ma-207	262	25	,	,	PUNCT
ma-207	262	26	14,17,18,21–35	14,17,18,21–35	NUM
ma-207	262	27	]	]	PUNCT
ma-207	262	28	.	.	PUNCT
ma-207	263	1	references	reference	NOUN
ma-207	263	2	[	[	X
ma-207	263	3	1	1	NUM
ma-207	263	4	]	]	PUNCT
ma-207	263	5	s.	s.	PROPN
ma-207	263	6	adly	adly	PROPN
ma-207	263	7	,	,	PUNCT
ma-207	263	8	h.	h.	PROPN
ma-207	263	9	van	van	PROPN
ma-207	263	10	ngai	ngai	PROPN
ma-207	263	11	,	,	PUNCT
ma-207	263	12	v.v	v.v	PROPN
ma-207	263	13	.	.	PROPN
ma-207	263	14	nguyen	nguyen	PROPN
ma-207	263	15	.	.	PUNCT
ma-207	264	1	newton	newton	PROPN
ma-207	264	2	’s	’s	PART
ma-207	264	3	method	method	NOUN
ma-207	264	4	for	for	ADP
ma-207	264	5	solving	solve	VERB
ma-207	264	6	generalized	generalized	ADJ
ma-207	264	7	equations	equation	NOUN
ma-207	264	8	:	:	PUNCT
ma-207	264	9	kantorovich	kantorovich	PROPN
ma-207	264	10	’s	’	NOUN
ma-207	264	11	and	and	CCONJ
ma-207	264	12	smale’sapproaches	smale’sapproache	NOUN
ma-207	264	13	.	.	PUNCT
ma-207	265	1	j.	j.	PROPN
ma-207	265	2	math	math	PROPN
ma-207	265	3	.	.	PUNCT
ma-207	266	1	anal	anal	PROPN
ma-207	266	2	.	.	PUNCT
ma-207	267	1	appl	appl	PROPN
ma-207	267	2	.	.	PUNCT
ma-207	268	1	439	439	NUM
ma-207	268	2	(	(	PUNCT
ma-207	268	3	2016	2016	NUM
ma-207	268	4	)	)	PUNCT
ma-207	268	5	,	,	PUNCT
ma-207	268	6	396–418	396–418	NUM
ma-207	268	7	.	.	PUNCT
ma-207	269	1	https://doi.org/10.1016/j.jmaa.2016.02.047.[2	https://doi.org/10.1016/j.jmaa.2016.02.047.[2	ADV
ma-207	269	2	]	]	X
ma-207	269	3	f.j	f.j	PROPN
ma-207	269	4	.	.	PROPN
ma-207	270	1	araǵon	araǵon	PROPN
ma-207	270	2	artacho	artacho	PROPN
ma-207	270	3	,	,	PUNCT
ma-207	270	4	a.	a.	NOUN
ma-207	270	5	belyakov	belyakov	PROPN
ma-207	270	6	,	,	PUNCT
ma-207	270	7	a.l	a.l	PROPN
ma-207	270	8	.	.	PROPN
ma-207	270	9	dontchev	dontchev	PROPN
ma-207	270	10	,	,	PUNCT
ma-207	270	11	m.	m.	NOUN
ma-207	270	12	lópez	lópez	PROPN
ma-207	270	13	.	.	PUNCT
ma-207	271	1	local	local	ADJ
ma-207	271	2	convergence	convergence	NOUN
ma-207	271	3	of	of	ADP
ma-207	271	4	quasi	quasi	ADJ
ma-207	271	5	-	-	ADJ
ma-207	271	6	newton	newton	PROPN
ma-207	271	7	methods	method	NOUN
ma-207	271	8	under	under	ADP
ma-207	271	9	metricregularity	metricregularity	NOUN
ma-207	271	10	.	.	PUNCT
ma-207	272	1	comput	comput	NOUN
ma-207	272	2	.	.	PUNCT
ma-207	273	1	optim	optim	PROPN
ma-207	273	2	.	.	PUNCT
ma-207	273	3	appl	appl	PROPN
ma-207	273	4	.	.	PUNCT
ma-207	274	1	58	58	NUM
ma-207	274	2	(	(	PUNCT
ma-207	274	3	2014	2014	NUM
ma-207	274	4	)	)	PUNCT
ma-207	274	5	,	,	PUNCT
ma-207	274	6	225–247	225–247	NUM
ma-207	274	7	.	.	PUNCT
ma-207	275	1	https://core.ac.uk/download/pdf/19775169.pdf.[3	https://core.ac.uk/download/pdf/19775169.pdf.[3	NOUN
ma-207	275	2	]	]	X
ma-207	276	1	f.j	f.j	PROPN
ma-207	276	2	.	.	PROPN
ma-207	276	3	aragón	aragón	PROPN
ma-207	276	4	artacho	artacho	PROPN
ma-207	276	5	,	,	PUNCT
ma-207	276	6	a.l	a.l	PROPN
ma-207	276	7	.	.	PROPN
ma-207	276	8	dontchev	dontchev	PROPN
ma-207	276	9	,	,	PUNCT
ma-207	276	10	m.	m.	NOUN
ma-207	276	11	gaydu	gaydu	PROPN
ma-207	276	12	,	,	PUNCT
ma-207	276	13	m.h	m.h	PROPN
ma-207	276	14	.	.	PROPN
ma-207	276	15	geoffroy	geoffroy	PROPN
ma-207	276	16	,	,	PUNCT
ma-207	276	17	v.m	v.m	PROPN
ma-207	276	18	.	.	PROPN
ma-207	276	19	veliov	veliov	PROPN
ma-207	276	20	.	.	PUNCT
ma-207	277	1	metric	metric	ADJ
ma-207	277	2	regularity	regularity	NOUN
ma-207	277	3	of	of	ADP
ma-207	277	4	newton	newton	PROPN
ma-207	277	5	’s	’s	PART
ma-207	277	6	itera	itera	NOUN
ma-207	277	7	-	-	PUNCT
ma-207	277	8	tion	tion	NOUN
ma-207	277	9	.	.	PUNCT
ma-207	278	1	siam	siam	PROPN
ma-207	278	2	j.	j.	PROPN
ma-207	278	3	control	control	PROPN
ma-207	278	4	optim	optim	PROPN
ma-207	278	5	.	.	PUNCT
ma-207	279	1	49	49	NUM
ma-207	279	2	(	(	PUNCT
ma-207	279	3	2011	2011	NUM
ma-207	279	4	)	)	PUNCT
ma-207	279	5	,	,	PUNCT
ma-207	279	6	339–362	339–362	NUM
ma-207	279	7	.	.	PUNCT
ma-207	280	1	https://nova.newcastle.edu.au/vital/access/services/	https://nova.newcastle.edu.au/vital/access/services/	PROPN
ma-207	280	2	download	download	NOUN
ma-207	280	3	/	/	SYM
ma-207	280	4	uon:11707	uon:11707	NOUN
ma-207	280	5	/	/	SYM
ma-207	280	6	attachment01.[4	attachment01.[4	PROPN
ma-207	280	7	]	]	X
ma-207	280	8	i.k	i.k	PROPN
ma-207	280	9	.	.	PROPN
ma-207	280	10	argyros	argyros	PROPN
ma-207	280	11	,	,	PUNCT
ma-207	280	12	convergence	convergence	NOUN
ma-207	280	13	and	and	CCONJ
ma-207	280	14	applications	application	NOUN
ma-207	280	15	of	of	ADP
ma-207	280	16	newton	newton	NOUN
ma-207	280	17	-	-	PUNCT
ma-207	280	18	type	type	NOUN
ma-207	280	19	iterations	iteration	NOUN
ma-207	280	20	,	,	PUNCT
ma-207	280	21	springer	springer	NOUN
ma-207	280	22	-	-	PUNCT
ma-207	280	23	verlag	verlag	PROPN
ma-207	280	24	,	,	PUNCT
ma-207	280	25	new	new	PROPN
ma-207	280	26	york	york	PROPN
ma-207	280	27	,	,	PUNCT
ma-207	280	28	2008.[5	2008.[5	NUM
ma-207	280	29	]	]	X
ma-207	280	30	i.k	i.k	PROPN
ma-207	280	31	.	.	PROPN
ma-207	280	32	argyros	argyros	PROPN
ma-207	280	33	,	,	PUNCT
ma-207	280	34	the	the	DET
ma-207	280	35	theory	theory	NOUN
ma-207	280	36	and	and	CCONJ
ma-207	280	37	application	application	NOUN
ma-207	280	38	of	of	ADP
ma-207	280	39	iteration	iteration	NOUN
ma-207	280	40	methods	method	NOUN
ma-207	280	41	,	,	PUNCT
ma-207	280	42	second	second	ADJ
ma-207	280	43	edition	edition	NOUN
ma-207	280	44	,	,	PUNCT
ma-207	280	45	engineering	engineering	NOUN
ma-207	280	46	series	series	NOUN
ma-207	280	47	,	,	PUNCT
ma-207	280	48	boca	boca	PROPN
ma-207	280	49	raton	raton	PROPN
ma-207	280	50	,	,	PUNCT
ma-207	280	51	florida	florida	PROPN
ma-207	280	52	,	,	PUNCT
ma-207	280	53	usa	usa	PROPN
ma-207	280	54	,	,	PUNCT
ma-207	280	55	2022	2022	NUM
ma-207	280	56	.	.	PUNCT
ma-207	281	1	https://doi.org/10.1201/9781003128915.[6	https://doi.org/10.1201/9781003128915.[6	NUM
ma-207	281	2	]	]	X
ma-207	281	3	i.k	i.k	PROPN
ma-207	281	4	.	.	PROPN
ma-207	281	5	argyros	argyros	PROPN
ma-207	281	6	,	,	PUNCT
ma-207	281	7	s.	s.	PROPN
ma-207	281	8	george	george	PROPN
ma-207	281	9	,	,	PUNCT
ma-207	281	10	on	on	ADP
ma-207	281	11	the	the	DET
ma-207	281	12	complexity	complexity	NOUN
ma-207	281	13	of	of	ADP
ma-207	281	14	extending	extend	VERB
ma-207	281	15	the	the	DET
ma-207	281	16	convergence	convergence	NOUN
ma-207	281	17	region	region	NOUN
ma-207	281	18	for	for	ADP
ma-207	281	19	traub	traub	PROPN
ma-207	281	20	’s	’s	PART
ma-207	281	21	method	method	NOUN
ma-207	281	22	,	,	PUNCT
ma-207	281	23	j.	j.	PROPN
ma-207	281	24	complex	complex	PROPN
ma-207	281	25	.	.	PUNCT
ma-207	282	1	56(2020	56(2020	NUM
ma-207	282	2	)	)	PUNCT
ma-207	282	3	,	,	PUNCT
ma-207	282	4	101423	101423	NUM
ma-207	282	5	.	.	PUNCT
ma-207	283	1	https://doi.org/10.1016/j.jco.2019.101423.[7	https://doi.org/10.1016/j.jco.2019.101423.[7	PROPN
ma-207	283	2	]	]	X
ma-207	283	3	l.	l.	PROPN
ma-207	283	4	blum	blum	PROPN
ma-207	283	5	,	,	PUNCT
ma-207	283	6	f.	f.	PROPN
ma-207	283	7	cucker	cucker	PROPN
ma-207	283	8	,	,	PUNCT
ma-207	283	9	m.	m.	NOUN
ma-207	283	10	shub	shub	NOUN
ma-207	283	11	,	,	PUNCT
ma-207	283	12	s.	s.	PROPN
ma-207	283	13	smale	smale	PROPN
ma-207	283	14	,	,	PUNCT
ma-207	283	15	complexity	complexity	NOUN
ma-207	283	16	and	and	CCONJ
ma-207	283	17	real	real	ADJ
ma-207	283	18	computation	computation	NOUN
ma-207	283	19	,	,	PUNCT
ma-207	283	20	springer	springer	NOUN
ma-207	283	21	-	-	PUNCT
ma-207	283	22	verlag	verlag	PROPN
ma-207	283	23	,	,	PUNCT
ma-207	283	24	ny	ny	PROPN
ma-207	283	25	,	,	PUNCT
ma-207	283	26	1998	1998	NUM
ma-207	283	27	.	.	PUNCT
ma-207	284	1	https	https	NOUN
ma-207	284	2	:	:	PUNCT
ma-207	285	1	//link.springer.com	//link.springer.com	PUNCT
ma-207	285	2	/	/	SYM
ma-207	285	3	book/10.1007/978	book/10.1007/978	ADJ
ma-207	285	4	-	-	PUNCT
ma-207	285	5	1	1	NUM
ma-207	285	6	-	-	PUNCT
ma-207	285	7	4612	4612	NUM
ma-207	285	8	-	-	PUNCT
ma-207	285	9	0701	0701	NUM
ma-207	285	10	-	-	PUNCT
ma-207	285	11	6.[8	6.[8	PROPN
ma-207	285	12	]	]	X
ma-207	285	13	j.f	j.f	PROPN
ma-207	285	14	.	.	PROPN
ma-207	285	15	bonnans	bonnan	NOUN
ma-207	285	16	,	,	PUNCT
ma-207	285	17	local	local	ADJ
ma-207	285	18	analysis	analysis	NOUN
ma-207	285	19	of	of	ADP
ma-207	285	20	newton	newton	NOUN
ma-207	285	21	-	-	PUNCT
ma-207	285	22	type	type	NOUN
ma-207	285	23	methods	method	NOUN
ma-207	285	24	for	for	ADP
ma-207	285	25	variational	variational	ADJ
ma-207	285	26	inequalities	inequality	NOUN
ma-207	285	27	and	and	CCONJ
ma-207	285	28	nonlinear	nonlinear	ADJ
ma-207	285	29	programming	programming	NOUN
ma-207	285	30	,	,	PUNCT
ma-207	285	31	appl.math	appl.math	PROPN
ma-207	285	32	.	.	PUNCT
ma-207	285	33	optim	optim	PROPN
ma-207	285	34	.	.	PUNCT
ma-207	286	1	29	29	NUM
ma-207	286	2	(	(	PUNCT
ma-207	286	3	1994	1994	NUM
ma-207	286	4	)	)	PUNCT
ma-207	286	5	,	,	PUNCT
ma-207	286	6	161	161	NUM
ma-207	286	7	-	-	SYM
ma-207	286	8	186	186	NUM
ma-207	286	9	.	.	PUNCT
ma-207	287	1	https://doi.org/10.1007/bf01204181.[9	https://doi.org/10.1007/bf01204181.[9	ADP
ma-207	287	2	]	]	X
ma-207	287	3	r.	r.	PROPN
ma-207	287	4	cibulka	cibulka	PROPN
ma-207	287	5	,	,	PUNCT
ma-207	287	6	a.	a.	NOUN
ma-207	287	7	dontchev	dontchev	PROPN
ma-207	287	8	,	,	PUNCT
ma-207	287	9	m.h	m.h	PROPN
ma-207	287	10	.	.	PROPN
ma-207	287	11	geoffroy	geoffroy	PROPN
ma-207	287	12	.	.	PUNCT
ma-207	288	1	inexact	inexact	ADJ
ma-207	288	2	newton	newton	PROPN
ma-207	288	3	methods	method	NOUN
ma-207	288	4	and	and	CCONJ
ma-207	288	5	dennismoŕe	dennismoŕe	VERB
ma-207	288	6	theorems	theorem	NOUN
ma-207	288	7	for	for	ADP
ma-207	288	8	nonsmooth	nonsmooth	ADJ
ma-207	288	9	gen	gen	PROPN
ma-207	288	10	-	-	ADJ
ma-207	288	11	eralized	eralize	VERB
ma-207	288	12	equations	equation	NOUN
ma-207	288	13	.	.	PUNCT
ma-207	289	1	siam	siam	PROPN
ma-207	289	2	j.	j.	PROPN
ma-207	289	3	control	control	PROPN
ma-207	289	4	optim	optim	PROPN
ma-207	289	5	.	.	PUNCT
ma-207	290	1	53	53	NUM
ma-207	290	2	(	(	PUNCT
ma-207	290	3	2015	2015	NUM
ma-207	290	4	)	)	PUNCT
ma-207	290	5	,	,	PUNCT
ma-207	290	6	1003–1019	1003–1019	NUM
ma-207	290	7	.	.	PUNCT
ma-207	291	1	https://doi.org/10.1137/140969476.[10	https://doi.org/10.1137/140969476.[10	PROPN
ma-207	291	2	]	]	SYM
ma-207	291	3	s.p	s.p	PROPN
ma-207	291	4	.	.	PROPN
ma-207	291	5	dokov	dokov	PROPN
ma-207	291	6	,	,	PUNCT
ma-207	291	7	a.l	a.l	PROPN
ma-207	291	8	.	.	PROPN
ma-207	291	9	dontchev	dontchev	PROPN
ma-207	291	10	,	,	PUNCT
ma-207	291	11	robinson	robinson	PROPN
ma-207	291	12	’s	’s	PART
ma-207	291	13	strong	strong	ADJ
ma-207	291	14	regularity	regularity	NOUN
ma-207	291	15	implies	imply	VERB
ma-207	291	16	robust	robust	ADJ
ma-207	291	17	local	local	ADJ
ma-207	291	18	convergence	convergence	NOUN
ma-207	291	19	of	of	ADP
ma-207	291	20	newton	newton	PROPN
ma-207	291	21	’s	’s	PART
ma-207	291	22	method	method	NOUN
ma-207	291	23	,	,	PUNCT
ma-207	291	24	appl.optim	appl.optim	PROPN
ma-207	291	25	.	.	PROPN
ma-207	291	26	(	(	PUNCT
ma-207	291	27	1998	1998	NUM
ma-207	291	28	)	)	PUNCT
ma-207	291	29	,	,	PUNCT
ma-207	291	30	116–129	116–129	NUM
ma-207	291	31	.	.	PUNCT
ma-207	292	1	https://doi.org/10.1007/978-1-4757-6095-8_6.[11	https://doi.org/10.1007/978-1-4757-6095-8_6.[11	PROPN
ma-207	292	2	]	]	X
ma-207	292	3	a.l	a.l	PROPN
ma-207	292	4	.	.	PROPN
ma-207	292	5	dontchev	dontchev	PROPN
ma-207	292	6	.	.	PUNCT
ma-207	293	1	local	local	ADJ
ma-207	293	2	convergence	convergence	NOUN
ma-207	293	3	of	of	ADP
ma-207	293	4	the	the	DET
ma-207	293	5	newton	newton	PROPN
ma-207	293	6	method	method	NOUN
ma-207	293	7	for	for	ADP
ma-207	293	8	generalized	generalized	ADJ
ma-207	293	9	equations	equation	NOUN
ma-207	293	10	.	.	PUNCT
ma-207	294	1	c.	c.	PROPN
ma-207	294	2	r.	r.	PROPN
ma-207	294	3	acad	acad	PROPN
ma-207	294	4	.	.	PUNCT
ma-207	295	1	sci	sci	PROPN
ma-207	295	2	.	.	PROPN
ma-207	295	3	paris	paris	PROPN
ma-207	295	4	ser	ser	PROPN
ma-207	295	5	.	.	PUNCT
ma-207	296	1	imath	imath	PROPN
ma-207	296	2	.	.	PUNCT
ma-207	297	1	322	322	NUM
ma-207	297	2	(	(	PUNCT
ma-207	297	3	1996	1996	NUM
ma-207	297	4	)	)	PUNCT
ma-207	297	5	,	,	PUNCT
ma-207	297	6	327–331.[12	327–331.[12	NOUN
ma-207	297	7	]	]	X
ma-207	297	8	a.l	a.l	PROPN
ma-207	297	9	.	.	PROPN
ma-207	297	10	dontchev	dontchev	PROPN
ma-207	297	11	,	,	PUNCT
ma-207	297	12	r.t	r.t	PROPN
ma-207	297	13	.	.	PROPN
ma-207	297	14	rockafellar	rockafellar	PROPN
ma-207	297	15	,	,	PUNCT
ma-207	297	16	characterizations	characterization	NOUN
ma-207	297	17	of	of	ADP
ma-207	297	18	strong	strong	ADJ
ma-207	297	19	regularity	regularity	NOUN
ma-207	297	20	for	for	ADP
ma-207	297	21	variational	variational	ADJ
ma-207	297	22	inequalities	inequality	NOUN
ma-207	297	23	over	over	ADP
ma-207	297	24	polyhedralconvex	polyhedralconvex	NOUN
ma-207	297	25	sets	set	NOUN
ma-207	297	26	,	,	PUNCT
ma-207	297	27	siam	siam	ADJ
ma-207	297	28	j.	j.	PROPN
ma-207	297	29	optim	optim	PROPN
ma-207	297	30	.	.	PROPN
ma-207	298	1	6	6	NUM
ma-207	298	2	(	(	PUNCT
ma-207	298	3	1996	1996	NUM
ma-207	298	4	)	)	PUNCT
ma-207	298	5	,	,	PUNCT
ma-207	298	6	1087	1087	NUM
ma-207	298	7	-	-	SYM
ma-207	298	8	1105	1105	NUM
ma-207	298	9	.	.	PUNCT
ma-207	299	1	https://doi.org/10.1137/s1052623495284029.[13	https://doi.org/10.1137/s1052623495284029.[13	X
ma-207	299	2	]	]	X
ma-207	299	3	a.l	a.l	PROPN
ma-207	299	4	.	.	PROPN
ma-207	299	5	dontchev	dontchev	PROPN
ma-207	299	6	,	,	PUNCT
ma-207	299	7	r.t	r.t	PROPN
ma-207	299	8	.	.	PROPN
ma-207	299	9	rockafellar	rockafellar	PROPN
ma-207	299	10	.	.	PUNCT
ma-207	300	1	newton	newton	PROPN
ma-207	300	2	’s	’s	PART
ma-207	300	3	method	method	NOUN
ma-207	300	4	for	for	ADP
ma-207	300	5	generalized	generalized	ADJ
ma-207	300	6	equations	equation	NOUN
ma-207	300	7	:	:	PUNCT
ma-207	300	8	a	a	DET
ma-207	300	9	sequential	sequential	ADJ
ma-207	300	10	implicit	implicit	ADJ
ma-207	300	11	function	function	NOUN
ma-207	300	12	theorem.math	theorem.math	PROPN
ma-207	300	13	.	.	PUNCT
ma-207	300	14	program	program	NOUN
ma-207	300	15	.	.	PUNCT
ma-207	301	1	123	123	NUM
ma-207	301	2	(	(	PUNCT
ma-207	301	3	2010	2010	NUM
ma-207	301	4	)	)	PUNCT
ma-207	301	5	,	,	PUNCT
ma-207	301	6	139–159	139–159	NUM
ma-207	301	7	.	.	PUNCT
ma-207	302	1	https://doi.org/10.1007/s10107-009-0322-5.[14	https://doi.org/10.1007/s10107-009-0322-5.[14	ADJ
ma-207	302	2	]	]	PUNCT
ma-207	302	3	a.	a.	NOUN
ma-207	302	4	l.	l.	PROPN
ma-207	302	5	dontchev	dontchev	PROPN
ma-207	302	6	and	and	CCONJ
ma-207	302	7	r.	r.	PROPN
ma-207	302	8	t.	t.	PROPN
ma-207	302	9	rockafellar	rockafellar	PROPN
ma-207	302	10	.	.	PUNCT
ma-207	303	1	convergence	convergence	NOUN
ma-207	303	2	of	of	ADP
ma-207	303	3	inexact	inexact	ADJ
ma-207	303	4	newton	newton	PROPN
ma-207	303	5	methods	method	NOUN
ma-207	303	6	for	for	ADP
ma-207	303	7	generalized	generalized	ADJ
ma-207	303	8	equations	equation	NOUN
ma-207	303	9	.	.	PUNCT
ma-207	304	1	math.program	math.program	NOUN
ma-207	304	2	.	.	NOUN
ma-207	304	3	139	139	NUM
ma-207	304	4	(	(	PUNCT
ma-207	304	5	2013	2013	NUM
ma-207	304	6	)	)	PUNCT
ma-207	304	7	,	,	PUNCT
ma-207	304	8	115–137.[15	115–137.[15	PROPN
ma-207	304	9	]	]	X
ma-207	304	10	a.l	a.l	PROPN
ma-207	304	11	.	.	PROPN
ma-207	304	12	dontchev	dontchev	PROPN
ma-207	304	13	,	,	PUNCT
ma-207	304	14	r.t	r.t	PROPN
ma-207	304	15	.	.	PROPN
ma-207	304	16	rockafellar	rockafellar	ADJ
ma-207	304	17	,	,	PUNCT
ma-207	304	18	implicit	implicit	ADJ
ma-207	304	19	functions	function	NOUN
ma-207	304	20	and	and	CCONJ
ma-207	304	21	solution	solution	NOUN
ma-207	304	22	mappings	mapping	NOUN
ma-207	304	23	:	:	PUNCT
ma-207	304	24	a	a	DET
ma-207	304	25	view	view	NOUN
ma-207	304	26	from	from	ADP
ma-207	304	27	variational	variational	ADJ
ma-207	304	28	analysis	analysis	NOUN
ma-207	304	29	,	,	PUNCT
ma-207	304	30	springer	springer	NOUN
ma-207	304	31	,	,	PUNCT
ma-207	304	32	new	new	PROPN
ma-207	304	33	york	york	PROPN
ma-207	304	34	,	,	PUNCT
ma-207	304	35	ny	ny	PROPN
ma-207	304	36	,	,	PUNCT
ma-207	304	37	2014	2014	NUM
ma-207	304	38	.	.	PUNCT
ma-207	305	1	https://doi.org/10.1007/978-1-4939-1037-3.[16	https://doi.org/10.1007/978-1-4939-1037-3.[16	PROPN
ma-207	305	2	]	]	PUNCT
ma-207	305	3	o.p	o.p	PROPN
ma-207	305	4	.	.	PROPN
ma-207	305	5	ferreira	ferreira	PROPN
ma-207	305	6	.	.	PUNCT
ma-207	306	1	local	local	ADJ
ma-207	306	2	convergence	convergence	NOUN
ma-207	306	3	of	of	ADP
ma-207	306	4	newton	newton	PROPN
ma-207	306	5	’s	’s	PART
ma-207	306	6	method	method	NOUN
ma-207	306	7	from	from	ADP
ma-207	306	8	the	the	DET
ma-207	306	9	view	view	NOUN
ma-207	306	10	point	point	NOUN
ma-207	306	11	of	of	ADP
ma-207	306	12	the	the	DET
ma-207	306	13	majorant	majorant	NOUN
ma-207	306	14	priciple	priciple	PROPN
ma-207	306	15	,	,	PUNCT
ma-207	306	16	i	i	PRON
ma-207	306	17	m	m	VERB
ma-207	306	18	a	a	PROPN
ma-207	306	19	j.	j.	PROPN
ma-207	306	20	numer.anal	numer.anal	PROPN
ma-207	306	21	.	.	PROPN
ma-207	306	22	29	29	NUM
ma-207	306	23	(	(	PUNCT
ma-207	306	24	2009	2009	NUM
ma-207	306	25	)	)	PUNCT
ma-207	306	26	,	,	PUNCT
ma-207	306	27	746	746	NUM
ma-207	306	28	-	-	SYM
ma-207	306	29	759.[17	759.[17	PROPN
ma-207	306	30	]	]	PUNCT
ma-207	306	31	a.a	a.a	PROPN
ma-207	306	32	.	.	PROPN
ma-207	306	33	magreńan	magreńan	PROPN
ma-207	306	34	,	,	PUNCT
ma-207	306	35	i.	i.	PROPN
ma-207	306	36	k.	k.	PROPN
ma-207	307	1	argyros	argyros	PROPN
ma-207	307	2	,	,	PUNCT
ma-207	307	3	a	a	DET
ma-207	307	4	contemporary	contemporary	ADJ
ma-207	307	5	study	study	NOUN
ma-207	307	6	of	of	ADP
ma-207	307	7	iterative	iterative	ADJ
ma-207	307	8	methods	method	NOUN
ma-207	307	9	:	:	PUNCT
ma-207	307	10	convergence	convergence	NOUN
ma-207	307	11	dynamics	dynamic	NOUN
ma-207	307	12	and	and	CCONJ
ma-207	307	13	applications	application	NOUN
ma-207	307	14	,	,	PUNCT
ma-207	307	15	academic	academic	ADJ
ma-207	307	16	press	press	NOUN
ma-207	307	17	,	,	PUNCT
ma-207	307	18	2018.[18	2018.[18	NUM
ma-207	307	19	]	]	X
ma-207	307	20	n.h	n.h	PROPN
ma-207	307	21	.	.	PROPN
ma-207	307	22	josephy	josephy	PROPN
ma-207	307	23	newton	newton	PROPN
ma-207	307	24	’s	’s	PART
ma-207	307	25	method	method	NOUN
ma-207	307	26	for	for	ADP
ma-207	307	27	generalized	generalized	ADJ
ma-207	307	28	equations	equation	NOUN
ma-207	307	29	,	,	PUNCT
ma-207	307	30	technical	technical	ADJ
ma-207	307	31	summary	summary	NOUN
ma-207	307	32	report	report	NOUN
ma-207	307	33	,	,	PUNCT
ma-207	307	34	mathematics	mathematics	PROPN
ma-207	307	35	research	research	NOUN
ma-207	307	36	center	center	NOUN
ma-207	307	37	,	,	PUNCT
ma-207	307	38	university	university	NOUN
ma-207	307	39	of	of	ADP
ma-207	307	40	wisconsin	wisconsin	PROPN
ma-207	307	41	,	,	PUNCT
ma-207	307	42	madison	madison	PROPN
ma-207	307	43	(	(	PUNCT
ma-207	307	44	1979	1979	NUM
ma-207	307	45	)	)	PUNCT
ma-207	307	46	.	.	PUNCT
ma-207	308	1	https://apps.dtic.mil/sti/citations/ada077096.[19	https://apps.dtic.mil/sti/citations/ada077096.[19	PROPN
ma-207	308	2	]	]	X
ma-207	308	3	j.	j.	PROPN
ma-207	308	4	nocedal	nocedal	PROPN
ma-207	308	5	,	,	PUNCT
ma-207	308	6	s.	s.	PROPN
ma-207	308	7	j.	j.	PROPN
ma-207	308	8	wright	wright	PROPN
ma-207	308	9	,	,	PUNCT
ma-207	308	10	numerical	numerical	PROPN
ma-207	308	11	optimization	optimization	NOUN
ma-207	308	12	,	,	PUNCT
ma-207	308	13	springer	springer	NOUN
ma-207	308	14	,	,	PUNCT
ma-207	308	15	ny	ny	PROPN
ma-207	308	16	,	,	PUNCT
ma-207	308	17	2006	2006	NUM
ma-207	308	18	.	.	PUNCT
ma-207	309	1	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-207	309	2	978	978	NUM
ma-207	309	3	-	-	SYM
ma-207	309	4	0	0	NUM
ma-207	309	5	-	-	PUNCT
ma-207	309	6	387	387	NUM
ma-207	309	7	-	-	PUNCT
ma-207	309	8	40065	40065	NUM
ma-207	309	9	-	-	PUNCT
ma-207	309	10	5[20	5[20	NUM
ma-207	309	11	]	]	X
ma-207	309	12	j.m	j.m	PROPN
ma-207	309	13	.	.	PROPN
ma-207	309	14	ortega	ortega	PROPN
ma-207	309	15	,	,	PUNCT
ma-207	309	16	w.c	w.c	PROPN
ma-207	309	17	.	.	PROPN
ma-207	309	18	rheinboldt	rheinboldt	ADJ
ma-207	309	19	,	,	PUNCT
ma-207	309	20	iterative	iterative	ADJ
ma-207	309	21	solution	solution	NOUN
ma-207	309	22	of	of	ADP
ma-207	309	23	nonlinear	nonlinear	ADJ
ma-207	309	24	equations	equation	NOUN
ma-207	309	25	in	in	ADP
ma-207	309	26	several	several	ADJ
ma-207	309	27	variables	variable	NOUN
ma-207	309	28	,	,	PUNCT
ma-207	309	29	academic	academic	ADJ
ma-207	309	30	press	press	NOUN
ma-207	309	31	,	,	PUNCT
ma-207	309	32	newyork	newyork	PROPN
ma-207	309	33	,	,	PUNCT
ma-207	309	34	1970	1970	NUM
ma-207	309	35	.	.	PUNCT
ma-207	310	1	https://doi.org/10.1016/c2013-0-11263-9	https://doi.org/10.1016/c2013-0-11263-9	PROPN
ma-207	310	2	.	.	PUNCT
ma-207	311	1	https://doi.org/10.28924/ada/ma.4.3	https://doi.org/10.28924/ada/ma.4.3	PROPN
ma-207	311	2	https://doi.org/10.1016/j.jmaa.2016.02.047	https://doi.org/10.1016/j.jmaa.2016.02.047	PROPN
ma-207	311	3	https://core.ac.uk/download/pdf/19775169.pdf	https://core.ac.uk/download/pdf/19775169.pdf	PROPN
ma-207	311	4	https://nova.newcastle.edu.au/vital/access/services/download/uon:11707/attachment01	https://nova.newcastle.edu.au/vital/access/services/download/uon:11707/attachment01	ADJ
ma-207	311	5	https://nova.newcastle.edu.au/vital/access/services/download/uon:11707/attachment01	https://nova.newcastle.edu.au/vital/access/services/download/uon:11707/attachment01	NOUN
ma-207	311	6	https://doi.org/10.1201/9781003128915	https://doi.org/10.1201/9781003128915	X
ma-207	311	7	https://doi.org/10.1016/j.jco.2019.101423	https://doi.org/10.1016/j.jco.2019.101423	PROPN
ma-207	311	8	https://link.springer.com/book/10.1007/978-1-4612-0701-6	https://link.springer.com/book/10.1007/978-1-4612-0701-6	PROPN
ma-207	311	9	https://link.springer.com/book/10.1007/978-1-4612-0701-6	https://link.springer.com/book/10.1007/978-1-4612-0701-6	PROPN
ma-207	311	10	https://doi.org/10.1007/bf01204181	https://doi.org/10.1007/bf01204181	X
ma-207	311	11	https://doi.org/10.1137/140969476	https://doi.org/10.1137/140969476	ADV
ma-207	311	12	https://doi.org/10.1007/978-1-4757-6095-8_6	https://doi.org/10.1007/978-1-4757-6095-8_6	PROPN
ma-207	311	13	https://doi.org/10.1137/s1052623495284029	https://doi.org/10.1137/s1052623495284029	PROPN
ma-207	311	14	https://doi.org/10.1007/s10107-009-0322-5	https://doi.org/10.1007/s10107-009-0322-5	NUM
ma-207	311	15	https://doi.org/10.1007/978-1-4939-1037-3	https://doi.org/10.1007/978-1-4939-1037-3	PROPN
ma-207	312	1	https://apps.dtic.mil/sti/citations/ada077096	https://apps.dtic.mil/sti/citations/ada077096	NOUN
ma-207	312	2	https://doi.org/10.1007/978-0-387-40065-5	https://doi.org/10.1007/978-0-387-40065-5	X
ma-207	312	3	https://doi.org/10.1007/978-0-387-40065-5	https://doi.org/10.1007/978-0-387-40065-5	PRON
ma-207	312	4	https://doi.org/10.1016/c2013-0-11263-9	https://doi.org/10.1016/c2013-0-11263-9	PROPN
ma-207	312	5	eur	eur	PROPN
ma-207	312	6	.	.	PUNCT
ma-207	313	1	j.	j.	PROPN
ma-207	313	2	math	math	PROPN
ma-207	313	3	.	.	PUNCT
ma-207	314	1	anal	anal	PROPN
ma-207	314	2	.	.	PUNCT
ma-207	315	1	10.28924	10.28924	NUM
ma-207	315	2	/	/	SYM
ma-207	315	3	ada	ada	PROPN
ma-207	315	4	/	/	PROPN
ma-207	315	5	ma.4.3	ma.4.3	PROPN
ma-207	315	6	10	10	NUM
ma-207	316	1	[	[	X
ma-207	316	2	21	21	NUM
ma-207	316	3	]	]	X
ma-207	316	4	p.d	p.d	PROPN
ma-207	316	5	.	.	PROPN
ma-207	316	6	proinov	proinov	PROPN
ma-207	316	7	,	,	PUNCT
ma-207	316	8	semi	semi	ADJ
ma-207	316	9	-	-	ADJ
ma-207	316	10	local	local	ADJ
ma-207	316	11	convergence	convergence	NOUN
ma-207	316	12	of	of	ADP
ma-207	316	13	two	two	NUM
ma-207	316	14	iterative	iterative	NOUN
ma-207	316	15	methods	method	NOUN
ma-207	316	16	for	for	ADP
ma-207	316	17	simultaneous	simultaneous	ADJ
ma-207	316	18	computation	computation	NOUN
ma-207	316	19	of	of	ADP
ma-207	316	20	polynomial	polynomial	ADJ
ma-207	316	21	zeros	zero	NOUN
ma-207	316	22	,	,	PUNCT
ma-207	316	23	c.r	c.r	PROPN
ma-207	316	24	.	.	PROPN
ma-207	316	25	acad	acad	PROPN
ma-207	316	26	.	.	PUNCT
ma-207	317	1	bulgare	bulgare	PROPN
ma-207	317	2	sci	sci	PROPN
ma-207	317	3	.	.	PROPN
ma-207	317	4	59	59	NUM
ma-207	317	5	(	(	PUNCT
ma-207	317	6	2006	2006	NUM
ma-207	317	7	)	)	PUNCT
ma-207	317	8	,	,	PUNCT
ma-207	317	9	705	705	NUM
ma-207	317	10	-	-	SYM
ma-207	317	11	712.[22	712.[22	X
ma-207	317	12	]	]	X
ma-207	317	13	p.d	p.d	PROPN
ma-207	317	14	.	.	PROPN
ma-207	317	15	proinov	proinov	PROPN
ma-207	317	16	,	,	PUNCT
ma-207	317	17	a	a	DET
ma-207	317	18	new	new	ADJ
ma-207	317	19	convergence	convergence	NOUN
ma-207	317	20	theorem	theorem	NOUN
ma-207	317	21	for	for	ADP
ma-207	317	22	the	the	DET
ma-207	317	23	weierstrass	weierstrass	NOUN
ma-207	317	24	method	method	NOUN
ma-207	317	25	from	from	ADP
ma-207	317	26	data	datum	NOUN
ma-207	317	27	at	at	ADP
ma-207	317	28	one	one	NUM
ma-207	317	29	point	point	NOUN
ma-207	317	30	,	,	PUNCT
ma-207	317	31	c.	c.	PROPN
ma-207	317	32	r.	r.	PROPN
ma-207	317	33	acad	acad	PROPN
ma-207	317	34	.	.	PUNCT
ma-207	318	1	bulgaresci	bulgaresci	PROPN
ma-207	318	2	.	.	PUNCT
ma-207	319	1	59	59	NUM
ma-207	319	2	(	(	PUNCT
ma-207	319	3	2006	2006	NUM
ma-207	319	4	)	)	PUNCT
ma-207	319	5	,	,	PUNCT
ma-207	320	1	131	131	NUM
ma-207	320	2	-	-	SYM
ma-207	320	3	136.[23	136.[23	NUM
ma-207	320	4	]	]	X
ma-207	320	5	s.m	s.m	PROPN
ma-207	320	6	.	.	PROPN
ma-207	320	7	robinson	robinson	PROPN
ma-207	320	8	,	,	PUNCT
ma-207	320	9	strongly	strongly	ADV
ma-207	320	10	regular	regular	ADJ
ma-207	320	11	generalized	generalized	ADJ
ma-207	320	12	equations	equation	NOUN
ma-207	320	13	,	,	PUNCT
ma-207	320	14	math	math	NOUN
ma-207	320	15	.	.	PUNCT
ma-207	321	1	oper	oper	PROPN
ma-207	321	2	.	.	PUNCT
ma-207	322	1	res	re	NOUN
ma-207	322	2	.	.	PROPN
ma-207	322	3	5	5	NUM
ma-207	322	4	(	(	PUNCT
ma-207	322	5	1980	1980	NUM
ma-207	322	6	)	)	PUNCT
ma-207	322	7	,	,	PUNCT
ma-207	322	8	43	43	NUM
ma-207	322	9	-	-	SYM
ma-207	322	10	62	62	NUM
ma-207	322	11	.	.	PUNCT
ma-207	323	1	https://www.jstor	https://www.jstor	NOUN
ma-207	323	2	.	.	PUNCT
ma-207	323	3	org	org	ADJ
ma-207	323	4	/	/	SYM
ma-207	323	5	stable/3689393.[24	stable/3689393.[24	NOUN
ma-207	323	6	]	]	X
ma-207	323	7	s.m	s.m	PROPN
ma-207	323	8	.	.	PROPN
ma-207	323	9	robinson	robinson	PROPN
ma-207	323	10	,	,	PUNCT
ma-207	323	11	generalized	generalized	ADJ
ma-207	323	12	equations	equation	NOUN
ma-207	323	13	,	,	PUNCT
ma-207	323	14	in	in	ADP
ma-207	323	15	:	:	PUNCT
ma-207	323	16	a.	a.	NOUN
ma-207	323	17	bachem	bachem	PROPN
ma-207	323	18	,	,	PUNCT
ma-207	323	19	b.	b.	PROPN
ma-207	323	20	korte	korte	PROPN
ma-207	323	21	,	,	PUNCT
ma-207	323	22	m.	m.	NOUN
ma-207	323	23	grötschel	grötschel	PROPN
ma-207	323	24	(	(	PUNCT
ma-207	323	25	eds	eds	PROPN
ma-207	323	26	.	.	PUNCT
ma-207	323	27	)	)	PUNCT
ma-207	323	28	,	,	PUNCT
ma-207	323	29	mathematical	mathematical	VERB
ma-207	323	30	programmingthe	programmingthe	DET
ma-207	323	31	state	state	NOUN
ma-207	323	32	of	of	ADP
ma-207	323	33	the	the	DET
ma-207	323	34	art	art	NOUN
ma-207	323	35	,	,	PUNCT
ma-207	323	36	springer	springer	NOUN
ma-207	323	37	berlin	berlin	PROPN
ma-207	323	38	heidelberg	heidelberg	PROPN
ma-207	323	39	,	,	PUNCT
ma-207	323	40	berlin	berlin	PROPN
ma-207	323	41	,	,	PUNCT
ma-207	323	42	heidelberg	heidelberg	PROPN
ma-207	323	43	,	,	PUNCT
ma-207	323	44	1983	1983	NUM
ma-207	323	45	:	:	PUNCT
ma-207	324	1	pp	pp	X
ma-207	324	2	.	.	PUNCT
ma-207	325	1	346	346	NUM
ma-207	325	2	-	-	SYM
ma-207	325	3	367	367	NUM
ma-207	325	4	.	.	PUNCT
ma-207	326	1	https://doi.org/10	https://doi.org/10	PROPN
ma-207	326	2	.	.	PUNCT
ma-207	327	1	1007/978	1007/978	NUM
ma-207	327	2	-	-	SYM
ma-207	327	3	3	3	NUM
ma-207	327	4	-	-	PUNCT
ma-207	327	5	642	642	NUM
ma-207	327	6	-	-	PUNCT
ma-207	327	7	68874	68874	NUM
ma-207	327	8	-	-	SYM
ma-207	327	9	4_14.[25	4_14.[25	NUM
ma-207	327	10	]	]	X
ma-207	327	11	s.m	s.m	PROPN
ma-207	327	12	.	.	PROPN
ma-207	327	13	robinson	robinson	PROPN
ma-207	327	14	,	,	PUNCT
ma-207	327	15	extension	extension	NOUN
ma-207	327	16	of	of	ADP
ma-207	327	17	newton	newton	PROPN
ma-207	327	18	’s	’s	PART
ma-207	327	19	method	method	NOUN
ma-207	327	20	to	to	ADP
ma-207	327	21	nonlinear	nonlinear	ADJ
ma-207	327	22	functions	function	NOUN
ma-207	327	23	with	with	ADP
ma-207	327	24	values	value	NOUN
ma-207	327	25	in	in	ADP
ma-207	327	26	a	a	DET
ma-207	327	27	cone	cone	NOUN
ma-207	327	28	,	,	PUNCT
ma-207	327	29	numer	numer	PROPN
ma-207	327	30	.	.	PROPN
ma-207	327	31	math	math	NOUN
ma-207	327	32	.	.	PUNCT
ma-207	328	1	19	19	NUM
ma-207	328	2	(	(	PUNCT
ma-207	328	3	1972),341	1972),341	NUM
ma-207	328	4	-	-	SYM
ma-207	328	5	347	347	NUM
ma-207	328	6	.	.	PUNCT
ma-207	329	1	https://doi.org/10.1007/bf01404880[26	https://doi.org/10.1007/bf01404880[26	NOUN
ma-207	329	2	]	]	PUNCT
ma-207	329	3	w.c	w.c	PROPN
ma-207	329	4	.	.	PROPN
ma-207	329	5	rheinboldt	rheinboldt	PROPN
ma-207	329	6	,	,	PUNCT
ma-207	329	7	an	an	DET
ma-207	329	8	adaptive	adaptive	ADJ
ma-207	329	9	continuation	continuation	NOUN
ma-207	329	10	process	process	NOUN
ma-207	329	11	for	for	ADP
ma-207	329	12	solving	solve	VERB
ma-207	329	13	systems	system	NOUN
ma-207	329	14	of	of	ADP
ma-207	329	15	nonlinear	nonlinear	ADJ
ma-207	329	16	equations	equation	NOUN
ma-207	329	17	,	,	PUNCT
ma-207	329	18	in	in	ADP
ma-207	329	19	:	:	PUNCT
ma-207	329	20	mathematicalmodels	mathematicalmodel	NOUN
ma-207	329	21	and	and	CCONJ
ma-207	329	22	numerical	numerical	ADJ
ma-207	329	23	methods	method	NOUN
ma-207	329	24	(	(	PUNCT
ma-207	329	25	a.n.tikhonov	a.n.tikhonov	VERB
ma-207	329	26	et	et	PROPN
ma-207	329	27	al	al	PROPN
ma-207	329	28	.	.	PUNCT
ma-207	329	29	eds	eds	PROPN
ma-207	329	30	.	.	PUNCT
ma-207	329	31	)	)	PUNCT
ma-207	330	1	pub.3	pub.3	PROPN
ma-207	330	2	,	,	PUNCT
ma-207	330	3	(	(	PUNCT
ma-207	330	4	1977	1977	NUM
ma-207	330	5	)	)	PUNCT
ma-207	330	6	,	,	PUNCT
ma-207	330	7	129	129	NUM
ma-207	330	8	-	-	SYM
ma-207	330	9	142	142	NUM
ma-207	330	10	banach	banach	NOUN
ma-207	330	11	center	center	NOUN
ma-207	330	12	,	,	PUNCT
ma-207	330	13	warsaw	warsaw	PROPN
ma-207	330	14	poland	poland	PROPN
ma-207	330	15	.	.	PUNCT
ma-207	331	1	https://eudml.org/doc/208686.[27	https://eudml.org/doc/208686.[27	PROPN
ma-207	331	2	]	]	X
ma-207	331	3	j.	j.	PROPN
ma-207	331	4	r.	r.	PROPN
ma-207	331	5	sharma	sharma	PROPN
ma-207	331	6	,	,	PUNCT
ma-207	331	7	a.	a.	PROPN
ma-207	331	8	arora	arora	PROPN
ma-207	331	9	,	,	PUNCT
ma-207	331	10	an	an	DET
ma-207	331	11	efficient	efficient	ADJ
ma-207	331	12	derivative	derivative	ADJ
ma-207	331	13	free	free	ADJ
ma-207	331	14	numerical	numerical	ADJ
ma-207	331	15	methods	method	NOUN
ma-207	331	16	for	for	ADP
ma-207	331	17	solving	solve	VERB
ma-207	331	18	systems	system	NOUN
ma-207	331	19	of	of	ADP
ma-207	331	20	nonlinear	nonlinear	ADJ
ma-207	331	21	equations	equation	NOUN
ma-207	331	22	,	,	PUNCT
ma-207	331	23	appl	appl	PROPN
ma-207	331	24	.	.	PROPN
ma-207	332	1	anal	anal	PROPN
ma-207	332	2	.	.	PUNCT
ma-207	333	1	disc	disc	PROPN
ma-207	333	2	.	.	PUNCT
ma-207	333	3	math	math	NOUN
ma-207	333	4	.	.	PUNCT
ma-207	334	1	7	7	NUM
ma-207	334	2	(	(	PUNCT
ma-207	334	3	2013	2013	NUM
ma-207	334	4	)	)	PUNCT
ma-207	334	5	,	,	PUNCT
ma-207	334	6	390	390	NUM
ma-207	334	7	-	-	SYM
ma-207	334	8	403	403	NUM
ma-207	334	9	.	.	PUNCT
ma-207	335	1	https://www.jstor.org/stable/43660724.[28	https://www.jstor.org/stable/43660724.[28	PROPN
ma-207	335	2	]	]	PUNCT
ma-207	335	3	j.r	j.r	PROPN
ma-207	335	4	.	.	PROPN
ma-207	335	5	sharma	sharma	PROPN
ma-207	335	6	,	,	PUNCT
ma-207	335	7	r.k	r.k	PROPN
ma-207	335	8	.	.	PROPN
ma-207	335	9	guha	guha	PROPN
ma-207	335	10	,	,	PUNCT
ma-207	335	11	r.	r.	PROPN
ma-207	335	12	sharma	sharma	PROPN
ma-207	335	13	,	,	PUNCT
ma-207	335	14	an	an	DET
ma-207	335	15	efficient	efficient	ADJ
ma-207	335	16	fourth	fourth	ADJ
ma-207	335	17	order	order	NOUN
ma-207	335	18	weighted	weight	VERB
ma-207	335	19	newton	newton	PROPN
ma-207	335	20	method	method	NOUN
ma-207	335	21	for	for	ADP
ma-207	335	22	systems	system	NOUN
ma-207	335	23	of	of	ADP
ma-207	335	24	nonlinearequations	nonlinearequation	NOUN
ma-207	335	25	,	,	PUNCT
ma-207	335	26	numer	numer	PROPN
ma-207	335	27	.	.	PROPN
ma-207	335	28	algor	algor	PROPN
ma-207	335	29	.	.	PUNCT
ma-207	336	1	62	62	NUM
ma-207	336	2	(	(	PUNCT
ma-207	336	3	2013	2013	NUM
ma-207	336	4	)	)	PUNCT
ma-207	336	5	,	,	PUNCT
ma-207	336	6	307	307	NUM
ma-207	336	7	-	-	SYM
ma-207	336	8	323	323	NUM
ma-207	336	9	.	.	PUNCT
ma-207	337	1	https://doi.org/10.1007/s11075-012-9585-7.[29	https://doi.org/10.1007/s11075-012-9585-7.[29	NOUN
ma-207	337	2	]	]	X
ma-207	337	3	s.m	s.m	PROPN
ma-207	337	4	.	.	PROPN
ma-207	337	5	shakhno	shakhno	PROPN
ma-207	337	6	,	,	PUNCT
ma-207	338	1	r.p	r.p	PROPN
ma-207	338	2	.	.	PROPN
ma-207	338	3	iakymchuk	iakymchuk	PROPN
ma-207	338	4	,	,	PUNCT
ma-207	338	5	h.p	h.p	PROPN
ma-207	338	6	.	.	PROPN
ma-207	338	7	yarmola	yarmola	PROPN
ma-207	338	8	,	,	PUNCT
ma-207	338	9	convergence	convergence	NOUN
ma-207	338	10	analysis	analysis	NOUN
ma-207	338	11	of	of	ADP
ma-207	338	12	a	a	DET
ma-207	338	13	two	two	NUM
ma-207	338	14	step	step	NOUN
ma-207	338	15	method	method	NOUN
ma-207	338	16	for	for	ADP
ma-207	338	17	the	the	DET
ma-207	338	18	nonlinear	nonlinear	ADJ
ma-207	338	19	squaresproblem	squaresproblem	NOUN
ma-207	338	20	with	with	ADP
ma-207	338	21	decomposition	decomposition	NOUN
ma-207	338	22	of	of	ADP
ma-207	338	23	operator	operator	NOUN
ma-207	338	24	,	,	PUNCT
ma-207	338	25	j.	j.	PROPN
ma-207	338	26	numer	numer	PROPN
ma-207	338	27	.	.	PUNCT
ma-207	338	28	appl	appl	PROPN
ma-207	338	29	.	.	PROPN
ma-207	338	30	math	math	PROPN
ma-207	338	31	.	.	PUNCT
ma-207	339	1	128	128	NUM
ma-207	339	2	(	(	PUNCT
ma-207	339	3	2018	2018	NUM
ma-207	339	4	)	)	PUNCT
ma-207	339	5	,	,	PUNCT
ma-207	339	6	82	82	NUM
ma-207	339	7	-	-	SYM
ma-207	339	8	95.[30	95.[30	PROPN
ma-207	339	9	]	]	X
ma-207	339	10	s.m	s.m	PROPN
ma-207	339	11	.	.	PROPN
ma-207	339	12	shakhno	shakhno	PROPN
ma-207	339	13	,	,	PUNCT
ma-207	339	14	o.p	o.p	PROPN
ma-207	339	15	.	.	PROPN
ma-207	339	16	gnatyshyn	gnatyshyn	PROPN
ma-207	339	17	,	,	PUNCT
ma-207	339	18	on	on	ADP
ma-207	339	19	an	an	DET
ma-207	339	20	iterative	iterative	ADJ
ma-207	339	21	algorithm	algorithm	NOUN
ma-207	339	22	of	of	ADP
ma-207	339	23	order	order	NOUN
ma-207	339	24	1.839	1.839	NUM
ma-207	339	25	for	for	ADP
ma-207	339	26	solving	solve	VERB
ma-207	339	27	the	the	DET
ma-207	339	28	nonlinear	nonlinear	ADJ
ma-207	339	29	least	least	ADJ
ma-207	339	30	squaresproblems	squaresproblem	NOUN
ma-207	339	31	,	,	PUNCT
ma-207	339	32	appl	appl	PROPN
ma-207	339	33	.	.	PROPN
ma-207	339	34	math	math	PROPN
ma-207	339	35	.	.	PUNCT
ma-207	340	1	comp	comp	NOUN
ma-207	340	2	.	.	PUNCT
ma-207	341	1	161	161	NUM
ma-207	341	2	(	(	PUNCT
ma-207	341	3	2005	2005	NUM
ma-207	341	4	)	)	PUNCT
ma-207	341	5	,	,	PUNCT
ma-207	341	6	253	253	NUM
ma-207	341	7	-	-	SYM
ma-207	341	8	264	264	NUM
ma-207	341	9	.	.	PUNCT
ma-207	342	1	https://doi.org/10.1016/j.amc.2003.12.025.[31	https://doi.org/10.1016/j.amc.2003.12.025.[31	PROPN
ma-207	342	2	]	]	PUNCT
ma-207	342	3	j.	j.	PROPN
ma-207	342	4	traub	traub	PROPN
ma-207	342	5	,	,	PUNCT
ma-207	342	6	iterative	iterative	NOUN
ma-207	342	7	methods	method	NOUN
ma-207	342	8	for	for	ADP
ma-207	342	9	solution	solution	NOUN
ma-207	342	10	of	of	ADP
ma-207	342	11	equations	equation	NOUN
ma-207	342	12	,	,	PUNCT
ma-207	342	13	prentice	prentice	NOUN
ma-207	342	14	-	-	PUNCT
ma-207	342	15	hall	hall	NOUN
ma-207	342	16	,	,	PUNCT
ma-207	342	17	englewood	englewood	PROPN
ma-207	342	18	cliffs	cliffs	PROPN
ma-207	342	19	,	,	PUNCT
ma-207	342	20	new	new	PROPN
ma-207	342	21	jersey	jersey	PROPN
ma-207	342	22	,	,	PUNCT
ma-207	342	23	usa	usa	PROPN
ma-207	342	24	,	,	PUNCT
ma-207	342	25	1964.[32	1964.[32	PROPN
ma-207	342	26	]	]	X
ma-207	342	27	j.	j.	PROPN
ma-207	342	28	traub	traub	PROPN
ma-207	342	29	,	,	PUNCT
ma-207	342	30	h.	h.	PROPN
ma-207	342	31	wozniakowski	wozniakowski	PROPN
ma-207	342	32	,	,	PUNCT
ma-207	342	33	convergence	convergence	NOUN
ma-207	342	34	and	and	CCONJ
ma-207	342	35	complexity	complexity	NOUN
ma-207	342	36	of	of	ADP
ma-207	342	37	newton	newton	PROPN
ma-207	342	38	iteration	iteration	PROPN
ma-207	342	39	for	for	ADP
ma-207	342	40	operator	operator	NOUN
ma-207	342	41	equations	equation	NOUN
ma-207	342	42	,	,	PUNCT
ma-207	342	43	j.	j.	PROPN
ma-207	342	44	assoc	assoc	PROPN
ma-207	342	45	.	.	PUNCT
ma-207	343	1	comp.math	comp.math	PROPN
ma-207	343	2	.	.	PROPN
ma-207	343	3	26	26	NUM
ma-207	343	4	(	(	PUNCT
ma-207	343	5	1979	1979	NUM
ma-207	343	6	)	)	PUNCT
ma-207	343	7	,	,	PUNCT
ma-207	343	8	250	250	NUM
ma-207	343	9	-	-	SYM
ma-207	343	10	258.[33	258.[33	NUM
ma-207	343	11	]	]	X
ma-207	343	12	j.	j.	PROPN
ma-207	343	13	wang	wang	PROPN
ma-207	343	14	and	and	CCONJ
ma-207	343	15	w.	w.	PROPN
ma-207	343	16	ouyang	ouyang	PROPN
ma-207	343	17	.	.	PUNCT
ma-207	344	1	newton	newton	PROPN
ma-207	344	2	’s	’s	PART
ma-207	344	3	method	method	NOUN
ma-207	344	4	for	for	ADP
ma-207	344	5	solving	solve	VERB
ma-207	344	6	generalized	generalized	ADJ
ma-207	344	7	equations	equation	NOUN
ma-207	344	8	without	without	ADP
ma-207	344	9	lipschitz	lipschitz	VERB
ma-207	344	10	condition	condition	NOUN
ma-207	344	11	.	.	PUNCT
ma-207	345	1	j.	j.	PROPN
ma-207	345	2	optim.theory	optim.theory	NOUN
ma-207	345	3	appl	appl	NOUN
ma-207	345	4	.	.	PUNCT
ma-207	346	1	192	192	NUM
ma-207	346	2	(	(	PUNCT
ma-207	346	3	2022	2022	NUM
ma-207	346	4	)	)	PUNCT
ma-207	346	5	,	,	PUNCT
ma-207	346	6	510–532	510–532	NUM
ma-207	346	7	.	.	PUNCT
ma-207	346	8	https://doi.org/10.1007/s10957-021-01974-0.[34	https://doi.org/10.1007/s10957-021-01974-0.[34	PROPN
ma-207	346	9	]	]	X
ma-207	346	10	y.	y.	NOUN
ma-207	346	11	nesterov	nesterov	PROPN
ma-207	346	12	and	and	CCONJ
ma-207	346	13	a.	a.	PROPN
ma-207	346	14	nemirovskii	nemirovskii	PROPN
ma-207	346	15	.	.	PUNCT
ma-207	347	1	interior	interior	ADJ
ma-207	347	2	-	-	PUNCT
ma-207	347	3	point	point	NOUN
ma-207	347	4	polynomial	polynomial	ADJ
ma-207	347	5	algorithms	algorithm	NOUN
ma-207	347	6	in	in	ADP
ma-207	347	7	convex	convex	NOUN
ma-207	347	8	programming	programming	NOUN
ma-207	347	9	.	.	PUNCT
ma-207	348	1	siam	siam	PROPN
ma-207	348	2	,	,	PUNCT
ma-207	348	3	1994	1994	NUM
ma-207	348	4	.	.	PUNCT
ma-207	349	1	https	https	NOUN
ma-207	349	2	:	:	PUNCT
ma-207	349	3	//doi.org/10.1137/1.9781611970791.[35	//doi.org/10.1137/1.9781611970791.[35	PROPN
ma-207	349	4	]	]	X
ma-207	349	5	p.p	p.p	PROPN
ma-207	349	6	.	.	PROPN
ma-207	349	7	zabrejko	zabrejko	PROPN
ma-207	349	8	,	,	PUNCT
ma-207	349	9	d.f	d.f	PROPN
ma-207	349	10	.	.	PROPN
ma-207	349	11	nguen	nguen	PROPN
ma-207	349	12	,	,	PUNCT
ma-207	349	13	the	the	DET
ma-207	349	14	majorant	majorant	NOUN
ma-207	349	15	method	method	NOUN
ma-207	349	16	in	in	ADP
ma-207	349	17	the	the	DET
ma-207	349	18	theory	theory	NOUN
ma-207	349	19	of	of	ADP
ma-207	349	20	newton	newton	PROPN
ma-207	349	21	-	-	PUNCT
ma-207	349	22	kantorovich	kantorovich	PROPN
ma-207	349	23	approximations	approximation	NOUN
ma-207	349	24	and	and	CCONJ
ma-207	349	25	the	the	DET
ma-207	349	26	ptákerror	ptákerror	NOUN
ma-207	349	27	estimates	estimate	NOUN
ma-207	349	28	,	,	PUNCT
ma-207	349	29	numer	numer	PROPN
ma-207	349	30	.	.	PUNCT
ma-207	350	1	funct	funct	PROPN
ma-207	350	2	.	.	PUNCT
ma-207	351	1	anal	anal	PROPN
ma-207	351	2	.	.	PUNCT
ma-207	352	1	optim	optim	PROPN
ma-207	352	2	.	.	PUNCT
ma-207	353	1	9	9	NUM
ma-207	353	2	(	(	PUNCT
ma-207	353	3	1987	1987	NUM
ma-207	353	4	)	)	PUNCT
ma-207	353	5	,	,	PUNCT
ma-207	353	6	671	671	NUM
ma-207	353	7	-	-	SYM
ma-207	353	8	684	684	NUM
ma-207	353	9	.	.	PUNCT
ma-207	354	1	https://doi.org/10.1080/01630568708816254	https://doi.org/10.1080/01630568708816254	ADJ
ma-207	354	2	.	.	PUNCT
ma-207	355	1	https://doi.org/10.28924/ada/ma.4.3	https://doi.org/10.28924/ada/ma.4.3	PROPN
ma-207	355	2	https://www.jstor.org/stable/3689393	https://www.jstor.org/stable/3689393	PROPN
ma-207	355	3	https://www.jstor.org/stable/3689393	https://www.jstor.org/stable/3689393	PROPN
ma-207	355	4	https://doi.org/10.1007/978-3-642-68874-4_14	https://doi.org/10.1007/978-3-642-68874-4_14	PROPN
ma-207	355	5	https://doi.org/10.1007/978-3-642-68874-4_14	https://doi.org/10.1007/978-3-642-68874-4_14	PROPN
ma-207	355	6	https://doi.org/10.1007/bf01404880	https://doi.org/10.1007/bf01404880	PRON
ma-207	355	7	https://eudml.org/doc/208686	https://eudml.org/doc/208686	CCONJ
ma-207	355	8	https://www.jstor.org/stable/43660724	https://www.jstor.org/stable/43660724	NOUN
ma-207	355	9	https://doi.org/10.1007/s11075-012-9585-7	https://doi.org/10.1007/s11075-012-9585-7	NUM
ma-207	355	10	https://doi.org/10.1016/j.amc.2003.12.025	https://doi.org/10.1016/j.amc.2003.12.025	PROPN
ma-207	355	11	https://doi.org/10.1007/s10957-021-01974-0	https://doi.org/10.1007/s10957-021-01974-0	NUM
ma-207	356	1	https://doi.org/10.1137/1.9781611970791	https://doi.org/10.1137/1.9781611970791	NOUN
ma-207	356	2	https://doi.org/10.1137/1.9781611970791	https://doi.org/10.1137/1.9781611970791	SYM
ma-207	356	3	https://doi.org/10.1080/01630568708816254	https://doi.org/10.1080/01630568708816254	PROPN
ma-207	356	4	1	1	NUM
ma-207	356	5	.	.	PUNCT
ma-207	357	1	introduction	introduction	NOUN
ma-207	357	2	2	2	NUM
ma-207	357	3	.	.	PUNCT
ma-207	357	4	mathematical	mathematical	ADJ
ma-207	357	5	bachground	bachground	PROPN
ma-207	357	6	3	3	PROPN
ma-207	357	7	.	.	PUNCT
ma-207	357	8	convergence	convergence	NOUN
ma-207	357	9	4	4	NUM
ma-207	357	10	.	.	PUNCT
ma-207	358	1	conclusion	conclusion	NOUN
ma-207	358	2	references	reference	NOUN