id	sid	eid	entity	type
ma-255	1	1	2025	CARDINAL
ma-255	2	1	j. math	PERSON
ma-255	4	1	5 (	CARDINAL
ma-255	5	1	5doi	CARDINAL
ma-255	5	2	10.28924	CARDINAL
ma-255	5	3	ioannis k. argyros1,∗	PERSON
ma-255	5	4	santhosh george2	PERSON
ma-255	5	5	regmi3	ORG
ma-255	5	6	michael i. argyros4	PERSON
ma-255	6	1	cameron university	ORG
ma-255	6	2	lawton	GPE
ma-255	7	1	2department	TIME
ma-255	7	2	national institute of technology karnataka	ORG
ma-255	7	3	025	CARDINAL
ma-255	7	4	university of houston	ORG
ma-255	7	5	houston	GPE
ma-255	7	6	tx	GPE
ma-255	7	7	77204	DATE
ma-255	7	8	4department of computer science	ORG
ma-255	7	9	university of oklahoma	ORG
ma-255	7	10	norman	GPE
ma-255	7	11	73501	DATE
ma-255	7	12	usa argyro01@email.franklin.edu	PERSON
ma-255	14	1	1	CARDINAL
ma-255	14	2	ω ⊂ x	ORG
ma-255	16	1	3	CARDINAL
ma-255	16	2	8	DATE
ma-255	16	3	14	DATE
ma-255	17	1	0	CARDINAL
ma-255	18	1	1.1	CARDINAL
ma-255	19	1	1.1	CARDINAL
ma-255	20	1	3 jul 2024	CARDINAL
ma-255	23	1	1	CARDINAL
ma-255	24	1	j. math	PERSON
ma-255	26	1	10.28924	CARDINAL
ma-255	26	2	2look	CARDINAL
ma-255	26	3	newton	GPE
ma-255	26	4	0	CARDINAL
ma-255	26	5	1	DATE
ma-255	26	6	2	DATE
ma-255	26	7	x0 ∈ ω	ORG
ma-255	26	8	1.2	CARDINAL
ma-255	26	9	∈ l(x	PERSON
ma-255	26	10	0	CARDINAL
ma-255	26	11	1	DATE
ma-255	26	12	2	CARDINAL
ma-255	27	1	newton	ORG
ma-255	32	1	f1	PERSON
ma-255	32	2	22,25].many	CARDINAL
ma-255	37	1	γ ∈ l(x	PERSON
ma-255	37	2	γ−1 ∈ l(y	ORG
ma-255	37	3	∈ l(y	PERSON
ma-255	38	1	newton	GPE
ma-255	40	1	1.3	CARDINAL
ma-255	43	1	1.4	CARDINAL
ma-255	44	1	= mp(x	PERSON
ma-255	47	1	1.3	CARDINAL
ma-255	47	2	x0 ∈ ω	ORG
ma-255	48	1	1.5	CARDINAL
ma-255	48	2	1.5	CARDINAL
ma-255	48	3	1.3	CARDINAL
ma-255	48	4	1.4	CARDINAL
ma-255	50	1	∈ ω	ORG
ma-255	51	1	1.5	CARDINAL
ma-255	51	2	m−1(xn − xn+1	PERSON
ma-255	51	3	0	CARDINAL
ma-255	55	1	j. math	PERSON
ma-255	57	1	10.28924	CARDINAL
ma-255	57	2	3i.e	CARDINAL
ma-255	58	1	0	CARDINAL
ma-255	59	1	1.1	CARDINAL
ma-255	62	1	x0 ∈ ω	ORG
ma-255	63	1	1.6	CARDINAL
ma-255	63	2	1.6	CARDINAL
ma-255	63	3	1.5	CARDINAL
ma-255	64	1	1.5	CARDINAL
ma-255	64	2	section 2	LAW
ma-255	65	1	two	CARDINAL
ma-255	66	1	first	ORDINAL
ma-255	66	2	x0	ORG
ma-255	68	1	1.6	CARDINAL
ma-255	70	1	theconvergence	PERSON
ma-255	70	2	5	CARDINAL
ma-255	70	3	6	DATE
ma-255	70	4	9	DATE
ma-255	70	5	18	CARDINAL
ma-255	71	1	29,30,34	CARDINAL
ma-255	72	1	1.5	CARDINAL
ma-255	73	1	0	CARDINAL
ma-255	74	1	1.7	CARDINAL
ma-255	74	2	section 3	LAW
ma-255	77	1	3	CARDINAL
ma-255	78	1	1.8	CARDINAL
ma-255	78	2	1–4	CARDINAL
ma-255	78	3	13	DATE
ma-255	78	4	17–19	CARDINAL
ma-255	78	5	21–23	CARDINAL
ma-255	78	6	26	DATE
ma-255	78	7	28	DATE
ma-255	78	8	32	DATE
ma-255	78	9	35	CARDINAL
ma-255	79	1	1.8	CARDINAL
ma-255	80	1	1.8	CARDINAL
ma-255	81	1	1–4,13,17–19,21–23,26,28,32,35	CARDINAL
ma-255	82	1	1.8	CARDINAL
ma-255	83	1	3 0	DATE
ma-255	83	2	1.9	CARDINAL
ma-255	84	1	∂f1(xn	GPE
ma-255	84	2	9	CARDINAL
ma-255	84	3	11	DATE
ma-255	84	4	23	DATE
ma-255	84	5	24	CARDINAL
ma-255	86	1	1.7	CARDINAL
ma-255	86	2	3	CARDINAL
ma-255	86	3	1.10	CARDINAL
ma-255	86	4	1.10	CARDINAL
ma-255	86	5	section 3	LAW
ma-255	86	6	section 2	LAW
ma-255	86	7	1.5	CARDINAL
ma-255	86	8	1.7	CARDINAL
ma-255	87	1	section 4	LAW
ma-255	88	1	j. math	PERSON
ma-255	90	1	10.28924	CARDINAL
ma-255	90	2	4is	ORDINAL
ma-255	92	1	8, 11	DATE
ma-255	92	2	19	CARDINAL
ma-255	93	1	s(z	PERSON
ma-255	93	2	0	CARDINAL
ma-255	97	1	6=	DATE
ma-255	99	1	y ∈ f2(x	PERSON
ma-255	100	1	x0	ORG
ma-255	100	2	0	CARDINAL
ma-255	100	3	∩	PERSON
ma-255	100	4	× v2 dist(x	GPE
ma-255	101	1	h(x	PERSON
ma-255	102	1	1.11	CARDINAL
ma-255	102	2	x0	ORG
ma-255	103	1	reg(h	ORG
ma-255	103	2	x0/y0	ORG
ma-255	104	1	v2	PRODUCT
ma-255	105	1	section 5	LAW
ma-255	106	1	2	CARDINAL
ma-255	106	2	1.5	CARDINAL
ma-255	108	1	2.1	CARDINAL
ma-255	109	1	14	CARDINAL
ma-255	109	2	22	DATE
ma-255	109	3	30	DATE
ma-255	109	4	34	CARDINAL
ma-255	109	5	1	CARDINAL
ma-255	111	1	n=0	PERSON
ma-255	111	2	1−	LANGUAGE
ma-255	115	1	j. math	PERSON
ma-255	117	1	10.28924	CARDINAL
ma-255	117	2	5	CARDINAL
ma-255	117	3	2.1	CARDINAL
ma-255	118	1	14,22,30,34	CARDINAL
ma-255	119	1	un	ORG
ma-255	119	2	∀n ≥ 0	DATE
ma-255	119	3	2.1	CARDINAL
ma-255	121	1	limn−→∞ un	PERSON
ma-255	122	1	− un	PERSON
ma-255	122	2	un	ORG
ma-255	126	1	0,+∞).suppose(h1	ORG
ma-255	127	1	‖m(x)γ−1(f1(y)− f1(x)− γm−1(x))‖	ORG
ma-255	127	2	x0‖	DATE
ma-255	128	1	− x0‖	PERSON
ma-255	129	1	− x‖	PERSON
ma-255	129	2	‖m(x0)γ−1f1(x0)‖	ORG
ma-255	129	3	0	CARDINAL
ma-255	129	4	1	DATE
ma-255	129	5	2	DATE
ma-255	131	1	1	CARDINAL
ma-255	131	2	2	DATE
ma-255	131	3	2.2	CARDINAL
ma-255	131	4	η	ORG
ma-255	132	1	2.2	CARDINAL
ma-255	132	2	1.5)in	CARDINAL
ma-255	132	3	2.3	CARDINAL
ma-255	133	1	η	GPE
ma-255	133	2	0	CARDINAL
ma-255	133	3	1	DATE
ma-255	133	4	2	DATE
ma-255	133	5	φ(αn−1	PERSON
ma-255	134	1	2.2	CARDINAL
ma-255	134	2	0 ≤ αn−1 ≤	MONEY
ma-255	135	1	η	GPE
ma-255	138	1	and(h3	NORP
ma-255	139	1	1.5	CARDINAL
ma-255	141	1	j. math	PERSON
ma-255	143	1	10.28924	CARDINAL
ma-255	143	2	6	CARDINAL
ma-255	143	3	2.1	CARDINAL
ma-255	145	1	1.5	CARDINAL
ma-255	145	2	0	CARDINAL
ma-255	145	3	1	DATE
ma-255	145	4	2	DATE
ma-255	145	5	∈	ORG
ma-255	145	6	0	CARDINAL
ma-255	146	1	0	CARDINAL
ma-255	146	2	1	DATE
ma-255	146	3	2	CARDINAL
ma-255	148	1	2.3	CARDINAL
ma-255	151	1	0	CARDINAL
ma-255	151	2	1	DATE
ma-255	151	3	2	CARDINAL
ma-255	152	1	2.4	CARDINAL
ma-255	152	2	η	GPE
ma-255	152	3	2.2	CARDINAL
ma-255	152	4	1.5	CARDINAL
ma-255	153	1	‖m(x0)γ−1f1(x0)‖ ≤ η	ORG
ma-255	153	2	2.4	CARDINAL
ma-255	154	1	x0	ORG
ma-255	154	2	2.4	CARDINAL
ma-255	154	3	m− 1	PERSON
ma-255	154	4	xm+1	PERSON
ma-255	154	5	1.5	CARDINAL
ma-255	154	6	γ.	GPE
ma-255	154	7	1.5	CARDINAL
ma-255	155	1	2.5	CARDINAL
ma-255	155	2	1.5	CARDINAL
ma-255	155	3	2.2	CARDINAL
ma-255	155	4	2.5	CARDINAL
ma-255	155	5	= ‖mγ−1(f1(xm)− f1(xm−1)− γm−1(xm − xm−1))‖ ≤ φ(‖xm−1	PERSON
ma-255	157	1	− x0‖	PERSON
ma-255	158	1	xm−1‖ ≤	DATE
ma-255	159	1	αm+1	DATE
ma-255	159	2	2.6	CARDINAL
ma-255	159	3	x0‖	DATE
ma-255	161	1	− xm−1‖+	PERSON
ma-255	164	1	2.4	CARDINAL
ma-255	164	2	xm+1} ⊂	PERCENT
ma-255	164	3	s(x0	PERSON
ma-255	165	1	estimate(2.4	DATE
ma-255	165	2	xm	ORG
ma-255	166	1	∈	ORG
ma-255	167	1	2.6	CARDINAL
ma-255	168	1	j. math	PERSON
ma-255	170	1	10.28924	CARDINAL
ma-255	171	1	0	CARDINAL
ma-255	172	1	0 = m−1(0	PERCENT
ma-255	173	1	mγ−1f1(xm	PERSON
ma-255	174	1	mm−1γ−1f1(xm	ORG
ma-255	175	1	= lim m→+∞	PERSON
ma-255	175	2	γ−1f1(xm	ORG
ma-255	176	1	lim	PERSON
ma-255	177	1	f1(s∗	GPE
ma-255	177	2	0	CARDINAL
ma-255	177	3	γ(0	GPE
ma-255	178	1	0	CARDINAL
ma-255	178	2	1	DATE
ma-255	178	3	2	CARDINAL
ma-255	179	1	2.4	CARDINAL
ma-255	181	1	2.7	CARDINAL
ma-255	181	2	2.7	CARDINAL
ma-255	181	3	2.3	CARDINAL
ma-255	182	1	w ∈	ORG
ma-255	182	2	inturn	PERSON
ma-255	182	3	‖(mγ−1)(γm−1)(w −	ORG
ma-255	182	4	γm−1(w − s∗))‖ ≤ φ(‖s∗ − x0‖	ORG
ma-255	182	5	x0‖	ORDINAL
ma-255	182	6	φ(α∗	PRODUCT
ma-255	183	1	2.1	CARDINAL
ma-255	184	1	22	CARDINAL
ma-255	185	1	∈	ORG
ma-255	185	2	0	CARDINAL
ma-255	185	3	12	DATE
ma-255	185	4	‖a‖	GPE
ma-255	187	1	− x0‖	PERSON
ma-255	188	1	− x0‖	PERSON
ma-255	189	1	− x‖	PERSON
ma-255	190	1	1 1−a	CARDINAL
ma-255	191	1	1−	TIME
ma-255	191	2	1−	TIME
ma-255	191	3	1 1−	TIME
ma-255	192	1	2.8	CARDINAL
ma-255	192	2	2.1	CARDINAL
ma-255	194	1	1− ap 1−	TIME
ma-255	195	1	‖m−1‖	ORG
ma-255	195	2	1−	TIME
ma-255	195	3	1− 2a	CARDINAL
ma-255	197	1	j. math	PERSON
ma-255	199	1	10.28924	CARDINAL
ma-255	199	2	8	CARDINAL
ma-255	200	1	φ	ORG
ma-255	201	1	ψ(t)− 1	LAW
ma-255	202	1	s∗ ∈ ω	ORG
ma-255	202	2	∈ ω ‖mγ−1(f1(x)−	ORG
ma-255	203	1	h6	ORG
ma-255	205	1	1.5	CARDINAL
ma-255	206	1	2.2	CARDINAL
ma-255	207	1	h6	ORG
ma-255	208	1	x0 ∈ s(s∗	ORG
ma-255	208	2	s(s∗	GPE
ma-255	208	3	s(s∗	GPE
ma-255	208	4	ψ(‖xn	ORG
ma-255	210	1	2.9	CARDINAL
ma-255	210	2	0	CARDINAL
ma-255	210	3	u(s∗	GPE
ma-255	212	1	xm+1	PERSON
ma-255	212	2	1.5	CARDINAL
ma-255	213	1	xm+1 −	PERSON
ma-255	216	1	γm−1(xm −	ORG
ma-255	217	1	2.10	CARDINAL
ma-255	217	2	2.10	CARDINAL
ma-255	219	1	2.11	CARDINAL
ma-255	220	1	0	CARDINAL
ma-255	220	2	1	CARDINAL
ma-255	220	3	2.9	CARDINAL
ma-255	220	4	1	CARDINAL
ma-255	220	5	2	DATE
ma-255	220	6	x0 ∈ s(s∗	ORG
ma-255	221	1	2.11	CARDINAL
ma-255	221	2	lim m→+∞xm	PERSON
ma-255	222	1	∈	ORG
ma-255	225	1	2.12	CARDINAL
ma-255	226	1	2.12	CARDINAL
ma-255	226	2	6=	CARDINAL
ma-255	227	1	j. math	PERSON
ma-255	229	1	10.28924	CARDINAL
ma-255	229	2	9	CARDINAL
ma-255	229	3	2.2	CARDINAL
ma-255	230	1	x0	ORG
ma-255	232	1	0	CARDINAL
ma-255	233	1	1.5	CARDINAL
ma-255	234	1	3	CARDINAL
ma-255	234	2	1.10	CARDINAL
ma-255	234	3	0	CARDINAL
ma-255	234	4	0	CARDINAL
ma-255	234	5	0	CARDINAL
ma-255	235	1	0	CARDINAL
ma-255	235	2	0	CARDINAL
ma-255	236	1	1	CARDINAL
ma-255	236	2	2	DATE
ma-255	237	1	− hn−1	PERSON
ma-255	238	1	3.1	CARDINAL
ma-255	238	2	3.2	CARDINAL
ma-255	239	1	∈	ORG
ma-255	240	1	0	CARDINAL
ma-255	240	2	0	CARDINAL
ma-255	240	3	1	DATE
ma-255	240	4	2	DATE
ma-255	242	1	3.1	CARDINAL
ma-255	242	2	0 ≤	MONEY
ma-255	243	1	h∗ ∈	ORG
ma-255	244	1	0	CARDINAL
ma-255	244	2	h∗	ORG
ma-255	244	3	x0 ∈ x	PERSON
ma-255	244	4	−→ qdn(x	PERSON
ma-255	244	5	− x0	PERSON
ma-255	245	1	+ f2(x	DATE
ma-255	245	2	3.2	CARDINAL
ma-255	245	3	x0	ORG
ma-255	246	1	− x0‖,	PERSON
ma-255	249	1	j. math	PERSON
ma-255	251	1	10.28924	CARDINAL
ma-255	251	2	10	CARDINAL
ma-255	251	3	3.1	CARDINAL
ma-255	252	1	1	CARDINAL
ma-255	252	2	1.10	CARDINAL
ma-255	252	3	0	CARDINAL
ma-255	252	4	1	DATE
ma-255	252	5	2	DATE
ma-255	252	6	∈	ORG
ma-255	252	7	1.8	CARDINAL
ma-255	253	1	3.3	CARDINAL
ma-255	254	1	3.4	CARDINAL
ma-255	254	2	0	CARDINAL
ma-255	254	3	1	DATE
ma-255	254	4	2	DATE
ma-255	255	1	1.10	CARDINAL
ma-255	256	1	3.1	CARDINAL
ma-255	257	1	11	CARDINAL
ma-255	257	2	2.2	CARDINAL
ma-255	258	1	1.10	CARDINAL
ma-255	258	2	c5	ORG
ma-255	258	3	1.9),(c4	CARDINAL
ma-255	259	1	− x0	PERSON
ma-255	263	1	0.λ	CARDINAL
ma-255	263	2	lim n→+∞w(t	PERSON
ma-255	264	1	0	CARDINAL
ma-255	265	1	γ ∈	ORG
ma-255	265	2	1	CARDINAL
ma-255	266	1	1− γ)min	TIME
ma-255	268	1	3.5	CARDINAL
ma-255	268	2	γ δ	ORG
ma-255	269	1	1	CARDINAL
ma-255	269	2	2	DATE
ma-255	269	3	satisfying(in	PERSON
ma-255	269	4	x0‖	CARDINAL
ma-255	269	5	1− γn)λ < λ.(iin	TIME
ma-255	270	1	− xn−1‖ ≤	PERSON
ma-255	271	1	∈	ORG
ma-255	275	1	dist(x0	ORG
ma-255	275	2	0	CARDINAL
ma-255	278	1	1− γ)λ	DATE
ma-255	280	1	j. math	PERSON
ma-255	282	1	10.28924	CARDINAL
ma-255	282	2	ma.5.5 11so	ORG
ma-255	282	3	xm	ORG
ma-255	283	1	xm+1	PERSON
ma-255	284	1	xm ∈	ORG
ma-255	284	2	xm).by	TIME
ma-255	285	1	c5	ORG
ma-255	285	2	x0	ORG
ma-255	289	1	− x0‖	PERSON
ma-255	289	2	− x0‖)‖x0 −	PERSON
ma-255	292	1	‖y0‖+ 1−	DATE
ma-255	292	2	1−	CARDINAL
ma-255	292	3	1− γm+1	TIME
ma-255	292	4	xm+1 = xm	PERSON
ma-255	293	1	dist(xm	NORP
ma-255	293	2	dist(em	GPE
ma-255	293	3	dist(em	GPE
ma-255	293	4	qdm(xm	GPE
ma-255	294	1	xm+1 ∈	PERSON
ma-255	294	2	dist(em	GPE
ma-255	294	3	qdm(xm	GPE
ma-255	295	1	qdm(xm	PERSON
ma-255	297	1	3	CARDINAL
ma-255	298	1	x0)−	GPE
ma-255	300	1	xm	ORG
ma-255	300	2	3.5	CARDINAL
ma-255	303	1	− x0	PERSON
ma-255	303	2	− xm−1	PERSON
ma-255	304	1	x0‖	ORDINAL
ma-255	304	2	− x0‖	PERSON
ma-255	306	1	3.6	CARDINAL
ma-255	308	1	− xm−1‖ ≤ γm‖x1 − x0‖ ≤	EVENT
ma-255	310	1	j. math	PERSON
ma-255	312	1	10.28924	CARDINAL
ma-255	312	2	12thus	CARDINAL
ma-255	312	3	+ 1	DATE
ma-255	312	4	∈	ORG
ma-255	314	1	− x0	PERSON
ma-255	315	1	+ 1	DATE
ma-255	315	2	x0‖	DATE
ma-255	317	1	x0‖ ≤	DATE
ma-255	317	2	γmβ1‖y0‖+	ORG
ma-255	317	3	1−	PRODUCT
ma-255	318	1	1−	CARDINAL
ma-255	321	1	1−	CARDINAL
ma-255	323	1	xm	ORG
ma-255	324	1	∈	PRODUCT
ma-255	325	1	1.8).set	CARDINAL
ma-255	328	1	xm	ORG
ma-255	329	1	x0‖	ORDINAL
ma-255	329	2	− x0‖	PERSON
ma-255	330	1	− hm−1)(αm	PERSON
ma-255	331	1	αm+1	CARDINAL
ma-255	332	1	xm	ORG
ma-255	332	2	ym)→	PERSON
ma-255	333	1	f1(s∗	GPE
ma-255	334	1	∗).finally	PERSON
ma-255	335	1	xm+1 isunique	PERSON
ma-255	335	2	xm	ORG
ma-255	337	1	1	CARDINAL
ma-255	338	1	1	CARDINAL
ma-255	338	2	r0.(c7	GPE
ma-255	338	3	∈	ORG
ma-255	338	4	1.8	CARDINAL
ma-255	339	1	∗	CARDINAL
ma-255	340	1	s(s∗	LOC
ma-255	340	2	0	CARDINAL
ma-255	340	3	0	CARDINAL
ma-255	340	4	1.10	CARDINAL
ma-255	342	1	j. math	PERSON
ma-255	344	1	10.28924	CARDINAL
ma-255	345	1	− xn‖)‖s∗	ORG
ma-255	346	1	3.7	CARDINAL
ma-255	346	2	x0 ∈ s(s∗	ORG
ma-255	347	1	1.10	CARDINAL
ma-255	348	1	3.2	CARDINAL
ma-255	350	1	1	CARDINAL
ma-255	350	2	1.10	CARDINAL
ma-255	350	3	s(s∗	LOC
ma-255	350	4	s(s∗	LOC
ma-255	350	5	0	CARDINAL
ma-255	350	6	1	CARDINAL
ma-255	350	7	2	CARDINAL
ma-255	352	1	x0‖	ORG
ma-255	353	1	0	CARDINAL
ma-255	353	2	1	CARDINAL
ma-255	354	1	tdn	PERSON
ma-255	354	2	s(s∗	LOC
ma-255	354	3	s(0	ORG
ma-255	354	4	1.8	CARDINAL
ma-255	356	1	3.1	CARDINAL
ma-255	356	2	γ ∈	ORG
ma-255	356	3	1)x0	CARDINAL
ma-255	356	4	3.6	CARDINAL
ma-255	356	5	3.7	CARDINAL
ma-255	356	6	3.6	CARDINAL
ma-255	361	1	xm ∈ s(s∗	ORG
ma-255	361	2	s(s∗	LOC
ma-255	361	3	xm	ORG
ma-255	361	4	xm−1	ORG
ma-255	362	1	4	CARDINAL
ma-255	362	2	x0	ORG
ma-255	362	3	4.1	CARDINAL
ma-255	363	1	0.1	CARDINAL
ma-255	363	2	0.3	CARDINAL
ma-255	364	1	+ 0.4	DATE
ma-255	364	2	+ 0.1	CARDINAL
ma-255	364	3	f1	PERSON
ma-255	364	4	f2	ORG
ma-255	366	1	y)t	DATE
ma-255	368	1	1− 0.1	CARDINAL
ma-255	368	2	0.3	CARDINAL
ma-255	368	3	0.2	CARDINAL
ma-255	369	1	0.1	CARDINAL
ma-255	371	1	1.2	CARDINAL
ma-255	375	1	j. math	PERSON
ma-255	377	1	10.28924	CARDINAL
ma-255	377	2	14	CARDINAL
ma-255	377	3	1.5	CARDINAL
ma-255	377	4	1	CARDINAL
ma-255	377	5	m1(x	PERSON
ma-255	382	1	4.1	CARDINAL
ma-255	383	1	1.5	CARDINAL
ma-255	383	2	2	CARDINAL
ma-255	386	1	4.2	CARDINAL
ma-255	387	1	1.5	CARDINAL
ma-255	387	2	3	CARDINAL
ma-255	390	1	4.3	CARDINAL
ma-255	391	1	1.5	CARDINAL
ma-255	391	2	4	CARDINAL
ma-255	395	1	−m4(x)f1(x	PERSON
ma-255	395	2	4.4	CARDINAL
ma-255	396	1	1.5	CARDINAL
ma-255	396	2	5	CARDINAL
ma-255	402	1	4.5	CARDINAL
ma-255	403	1	1.5	CARDINAL
ma-255	403	2	1	CARDINAL
ma-255	403	3	5	DATE
ma-255	403	4	4.6	CARDINAL
ma-255	406	1	1.5	CARDINAL
ma-255	406	2	newton	ORG
ma-255	406	3	1.2	CARDINAL
ma-255	407	1	1.5	CARDINAL
ma-255	407	2	newton	ORG
ma-255	408	1	1	CARDINAL
ma-255	408	2	4	CARDINAL
ma-255	408	3	3 to 5	CARDINAL
ma-255	408	4	newton	GPE
ma-255	410	1	j. math	PERSON
ma-255	412	1	10.28924	CARDINAL
ma-255	412	2	15	CARDINAL
ma-255	412	3	1.2	CARDINAL
ma-255	412	4	4	CARDINAL
ma-255	412	5	1.2	CARDINAL
ma-255	412	6	4	CARDINAL
ma-255	412	7	4.1	CARDINAL
ma-255	412	8	1 6	CARDINAL
ma-255	412	9	4.6	CARDINAL
ma-255	412	10	1 8	DATE
ma-255	412	11	4.2	CARDINAL
ma-255	412	12	2 5	DATE
ma-255	412	13	4.6	CARDINAL
ma-255	412	14	2 6	DATE
ma-255	412	15	4.3	CARDINAL
ma-255	412	16	3 4	DATE
ma-255	412	17	4.6	CARDINAL
ma-255	412	18	3 5	DATE
ma-255	412	19	4.4	CARDINAL
ma-255	412	20	4 4	DATE
ma-255	412	21	4.6	CARDINAL
ma-255	412	22	4 5	DATE
ma-255	412	23	4.5	CARDINAL
ma-255	412	24	5 4	DATE
ma-255	412	25	4.6	CARDINAL
ma-255	412	26	5	CARDINAL
ma-255	413	1	x0	ORG
ma-255	413	2	1	CARDINAL
ma-255	413	3	1	CARDINAL
ma-255	413	4	′1(x0)‖	ORG
ma-255	414	1	0.3129	CARDINAL
ma-255	414	2	1	CARDINAL
ma-255	414	3	1.2	CARDINAL
ma-255	414	4	3	CARDINAL
ma-255	414	5	1.2	CARDINAL
ma-255	414	6	3	CARDINAL
ma-255	414	7	4.1	CARDINAL
ma-255	414	8	1 5	CARDINAL
ma-255	414	9	4.6	CARDINAL
ma-255	414	10	1 3	DATE
ma-255	414	11	4.2	CARDINAL
ma-255	414	12	2 4	DATE
ma-255	414	13	4.6	CARDINAL
ma-255	414	14	2 3	DATE
ma-255	414	15	4.3	CARDINAL
ma-255	414	16	3 3	DATE
ma-255	414	17	4.6	CARDINAL
ma-255	414	18	3 3	DATE
ma-255	414	19	4.4	CARDINAL
ma-255	414	20	4 3	DATE
ma-255	414	21	4.6	CARDINAL
ma-255	414	22	4 3 (	DATE
ma-255	414	23	4.5	CARDINAL
ma-255	414	24	5 3	DATE
ma-255	414	25	4.6	CARDINAL
ma-255	414	26	5	CARDINAL
ma-255	415	1	x0	ORG
ma-255	415	2	0	CARDINAL
ma-255	415	3	0	DATE
ma-255	415	4	′1(x0)‖	ORG
ma-255	415	5	0.1414	CARDINAL
ma-255	415	6	1	CARDINAL
ma-255	415	7	1.2	CARDINAL
ma-255	415	8	5	CARDINAL
ma-255	415	9	1.2	CARDINAL
ma-255	415	10	5	CARDINAL
ma-255	415	11	4.1	CARDINAL
ma-255	415	12	1 7	DATE
ma-255	415	13	4.6	CARDINAL
ma-255	415	14	1 9	DATE
ma-255	415	15	4.2	CARDINAL
ma-255	415	16	2 5	DATE
ma-255	415	17	4.6	CARDINAL
ma-255	415	18	2 7	DATE
ma-255	415	19	4.3	CARDINAL
ma-255	415	20	3 5	DATE
ma-255	415	21	4.6	CARDINAL
ma-255	415	22	3 6	DATE
ma-255	415	23	4.4	CARDINAL
ma-255	415	24	4 5	DATE
ma-255	415	25	4.6	CARDINAL
ma-255	415	26	4 6	DATE
ma-255	415	27	4.5	CARDINAL
ma-255	415	28	5 5	DATE
ma-255	415	29	4.6	CARDINAL
ma-255	415	30	5	CARDINAL
ma-255	416	1	x0	ORG
ma-255	416	2	′1(x0)‖	ORG
ma-255	416	3	1	CARDINAL
ma-255	416	4	5	CARDINAL
ma-255	416	5	acoc	GPE
ma-255	416	6	1.5	CARDINAL
ma-255	416	7	newton	ORG
ma-255	416	8	1.2	CARDINAL
ma-255	417	1	4.1	CARDINAL
ma-255	419	1	j. math	PERSON
ma-255	421	1	10.28924	CARDINAL
ma-255	421	2	16	CARDINAL
ma-255	421	3	1.2	CARDINAL
ma-255	421	4	7	CARDINAL
ma-255	421	5	1.2	CARDINAL
ma-255	421	6	4.1	CARDINAL
ma-255	421	7	1 8	DATE
ma-255	421	8	4.6	CARDINAL
ma-255	421	9	1 12	CARDINAL
ma-255	421	10	4.2	CARDINAL
ma-255	421	11	2 7	DATE
ma-255	421	12	4.6	CARDINAL
ma-255	421	13	2 8	DATE
ma-255	421	14	4.3	CARDINAL
ma-255	421	15	3 7	DATE
ma-255	421	16	4.6	CARDINAL
ma-255	421	17	3 8	DATE
ma-255	421	18	4.4	CARDINAL
ma-255	421	19	4 7	DATE
ma-255	421	20	4.6	CARDINAL
ma-255	421	21	4 7	DATE
ma-255	421	22	4.5	CARDINAL
ma-255	421	23	5 7	DATE
ma-255	421	24	4.6	CARDINAL
ma-255	421	25	5	CARDINAL
ma-255	422	1	10−12	DATE
ma-255	422	2	x0	ORG
ma-255	422	3	′1(x0)‖	ORG
ma-255	422	4	1	CARDINAL
ma-255	423	1	xj−1	GPE
ma-255	423	2	xj	GPE
ma-255	423	3	three	CARDINAL
ma-255	424	1	6	CARDINAL
ma-255	425	1	4.2	CARDINAL
ma-255	426	1	êj = xj	PERSON
ma-255	427	1	xj−1	GPE
ma-255	428	1	xj	GPE
ma-255	428	2	xj−1	GPE
ma-255	428	3	three	CARDINAL
ma-255	428	4	6	CARDINAL
ma-255	429	1	1.2	CARDINAL
ma-255	429	2	4.1	CARDINAL
ma-255	429	3	1 0.863 1	CARDINAL
ma-255	429	4	4.2	CARDINAL
ma-255	429	5	2 0.2695 1.0438	CARDINAL
ma-255	429	6	4.3	CARDINAL
ma-255	429	7	3	CARDINAL
ma-255	429	8	4.4	CARDINAL
ma-255	429	9	4	CARDINAL
ma-255	429	10	4.5	CARDINAL
ma-255	429	11	5	CARDINAL
ma-255	429	12	4.6	CARDINAL
ma-255	429	13	1 0.9065 1.0118	CARDINAL
ma-255	429	14	4.6	CARDINAL
ma-255	429	15	2	CARDINAL
ma-255	429	16	4.6	CARDINAL
ma-255	429	17	3	CARDINAL
ma-255	429	18	4.6	CARDINAL
ma-255	429	19	4	CARDINAL
ma-255	429	20	4.6	CARDINAL
ma-255	430	1	x0	ORG
ma-255	430	2	10−12	DATE
ma-255	432	1	j. math	PERSON
ma-255	434	1	10.28924	CARDINAL
ma-255	434	2	17	CARDINAL
ma-255	434	3	5	CARDINAL
ma-255	434	4	newton	GPE
ma-255	434	5	4 to 5	CARDINAL
ma-255	434	6	2	CARDINAL
ma-255	434	7	4.2	CARDINAL
ma-255	435	1	ω	CARDINAL
ma-255	435	2	1	CARDINAL
ma-255	436	1	ω	ORG
ma-255	436	2	∈	ORG
ma-255	436	3	1	CARDINAL
ma-255	436	4	1 2	CARDINAL
ma-255	437	1	22,25	CARDINAL
ma-255	438	1	1	CARDINAL
ma-255	438	2	0	CARDINAL
ma-255	439	1	1)a3 + 1 	DATE
ma-255	440	1	0	CARDINAL
ma-255	440	2	0	CARDINAL
ma-255	440	3	0)tr	GPE
ma-255	441	1	0	CARDINAL
ma-255	442	1	2.2	CARDINAL
ma-255	442	2	1	CARDINAL
ma-255	442	3	ϕ(t	PERSON
ma-255	444	1	∈	ORG
ma-255	444	2	0	CARDINAL
ma-255	444	3	0.2909883534	ORG
ma-255	446	1	4.3	CARDINAL
ma-255	447	1	1	CARDINAL
ma-255	447	2	0	CARDINAL
ma-255	447	3	1	CARDINAL
ma-255	448	1	y = h[0	PERSON
ma-255	448	2	1	CARDINAL
ma-255	448	3	ω	CARDINAL
ma-255	448	4	1	CARDINAL
ma-255	449	1	0	CARDINAL
ma-255	450	1	f1	PERSON
ma-255	450	2	1	CARDINAL
ma-255	451	1	z(v)− 4	ORG
ma-255	451	2	1	CARDINAL
ma-255	451	3	f1 f	PERSON
ma-255	451	4	w(v)−	GPE
ma-255	451	5	12	CARDINAL
ma-255	451	6	1	CARDINAL
ma-255	452	1	2.2	CARDINAL
ma-255	452	2	0	CARDINAL
ma-255	453	1	1	CARDINAL
ma-255	453	2	ϕ(t	PERSON
ma-255	454	1	6	CARDINAL
ma-255	454	2	∈	ORG
ma-255	454	3	0	CARDINAL
ma-255	454	4	0.83̄	CARDINAL
ma-255	455	1	5	CARDINAL
ma-255	458	1	5–7,9	CARDINAL
ma-255	458	2	14,23,24,31	DATE
ma-255	460	1	mykhailo	PERSON
ma-255	460	2	ivan franko	PERSON
ma-255	460	3	national university of lviv	ORG
ma-255	460	4	lviv	GPE
ma-255	460	5	4.1	CARDINAL
ma-255	462	1	j. math	PERSON
ma-255	464	1	10.28924	CARDINAL
ma-255	465	1	1	CARDINAL
ma-255	465	2	r. cibulka	PERSON
ma-255	465	3	h.v. ngai	PERSON
ma-255	465	4	newton	GPE
ma-255	465	5	siam	GPE
ma-255	466	1	25	CARDINAL
ma-255	466	2	2015	CARDINAL
ma-255	466	3	159	CARDINAL
ma-255	466	4	h.v. ngai	PERSON
ma-255	466	5	n.v. vu	PERSON
ma-255	466	6	newton	GPE
ma-255	466	7	kantorovich	PERSON
ma-255	466	8	j. math	PERSON
ma-255	469	1	439	CARDINAL
ma-255	469	2	2016	CARDINAL
ma-255	469	3	396	CARDINAL
ma-255	469	4	allgower	PERSON
ma-255	469	5	k. georg	PERSON
ma-255	469	6	berlin	GPE
ma-255	469	7	heidelberg new york,1989.[4] f.j.	ORG
ma-255	469	8	aragón artacho	PERSON
ma-255	469	9	a. melyakov	PERSON
ma-255	469	10	a.l.	GPE
ma-255	469	11	dontchev	PERSON
ma-255	469	12	m. lopez	PERSON
ma-255	469	13	quasi-newton	ORG
ma-255	470	1	optim	PERSON
ma-255	471	1	58	CARDINAL
ma-255	471	2	2014	DATE
ma-255	471	3	225	CARDINAL
ma-255	471	4	newton	GPE
ma-255	471	5	berlin	GPE
ma-255	471	6	2008.[6	CARDINAL
ma-255	471	7	second	ORDINAL
ma-255	471	8	crc press	ORG
ma-255	471	9	taylorand francis	PERSON
ma-255	471	10	boca raton	GPE
ma-255	471	11	2002.[7	CARDINAL
ma-255	471	12	s. george	PERSON
ma-255	471	13	newton	GPE
ma-255	471	14	j. complex	PERSON
ma-255	472	1	81	CARDINAL
ma-255	472	2	2024	CARDINAL
ma-255	473	1	aubin	PERSON
ma-255	473	2	h. frankowska	PERSON
ma-255	473	3	boston	GPE
ma-255	473	4	1990.[9	CARDINAL
ma-255	473	5	e. catinas	PERSON
ma-255	473	6	quasi-newton	ORG
ma-255	475	1	74(2005	CARDINAL
ma-255	475	2	291	CARDINAL
ma-255	475	3	p.g.	GPE
ma-255	475	4	ciarlet	GPE
ma-255	475	5	c. mardare	PERSON
ma-255	475	6	newton-kantorovich	ORG
ma-255	477	1	10	CARDINAL
ma-255	477	2	2012	DATE
ma-255	477	3	249	CARDINAL
ma-255	477	4	r. cibulka	PERSON
ma-255	477	5	a.l.	GPE
ma-255	477	6	dontchev	PERSON
ma-255	477	7	j. preininger	PERSON
ma-255	477	8	t. roubal	PERSON
ma-255	477	9	v. veliov	PERSON
ma-255	477	10	j. convex	PERSON
ma-255	478	1	25	CARDINAL
ma-255	478	2	2018	DATE
ma-255	478	3	459	CARDINAL
ma-255	478	4	newton	GPE
ma-255	480	1	32	CARDINAL
ma-255	480	2	amer	PERSON
ma-255	481	1	1996	DATE
ma-255	482	1	295-306.[13	CARDINAL
ma-255	482	2	dontchev	GPE
ma-255	482	3	r.t. rockafellar	GPE
ma-255	482	4	,springer	NORP
ma-255	482	5	berlin	GPE
ma-255	482	6	2014.[14	ORG
ma-255	482	7	newton	ORG
ma-255	482	8	affine invariance	ORG
ma-255	482	9	35	DATE
ma-255	482	10	berlin	GPE
ma-255	482	11	2004.[15	GPE
ma-255	482	12	j.m. gutiérrez	GPE
ma-255	482	13	m.a. hernández	PERSON
ma-255	482	14	n. romero	PERSON
ma-255	482	15	m.j. rubio	PERSON
ma-255	482	16	newton	ORG
ma-255	482	17	newton	GPE
ma-255	482	18	spanish	NORP
ma-255	482	19	gac	ORG
ma-255	482	20	r. soc	PERSON
ma-255	485	1	13	CARDINAL
ma-255	485	2	2010	DATE
ma-255	485	3	53-76.[16	CARDINAL
ma-255	485	4	m.a. hernández-veron	PERSON
ma-255	485	5	newton	ORG
ma-255	486	1	lett	PERSON
ma-255	486	2	85	DATE
ma-255	486	3	2018	DATE
ma-255	486	4	48-56.[17	CARDINAL
ma-255	486	5	f. facchinei	PERSON
ma-255	487	1	2003.[18	ORG
ma-255	487	2	ferreira	GPE
ma-255	487	3	g.n. silva	PERSON
ma-255	487	4	newton	ORG
ma-255	488	1	1461	CARDINAL
ma-255	488	2	a.f. izmailov	ORG
ma-255	488	3	m.v.	GPE
ma-255	489	1	solodov	GPE
ma-255	489	2	newton	GPE
ma-255	489	3	berlin	GPE
ma-255	489	4	kelley	PERSON
ma-255	489	5	newton	ORG
ma-255	489	6	m. kummer	PERSON
ma-255	489	7	newton	GPE
ma-255	489	8	j. guddat et al	PERSON
ma-255	491	1	45	CARDINAL
ma-255	491	2	akademie-verlag	ORG
ma-255	491	3	berlin	GPE
ma-255	491	4	1988	DATE
ma-255	492	1	114-125.[22	CARDINAL
ma-255	492	2	l.v. kantorovich	ORG
ma-255	492	3	g. akilov	PERSON
ma-255	492	4	normed spaces	ORG
ma-255	492	5	pergamon press	ORG
ma-255	492	6	london	GPE
ma-255	492	7	moore	PERSON
ma-255	492	8	m.z. nashed	PERSON
ma-255	492	9	linear operators	ORG
ma-255	492	10	j. appl	PERSON
ma-255	493	1	27	CARDINAL
ma-255	493	2	1974)1-16.[24	DATE
ma-255	493	3	nashed	ORG
ma-255	493	4	new york	GPE
ma-255	493	5	1976	DATE
ma-255	495	1	j. math	PERSON
ma-255	497	1	10.28924	CARDINAL
ma-255	497	2	19	CARDINAL
ma-255	497	3	25	CARDINAL
ma-255	497	4	103	DATE
ma-255	497	5	pitman	GPE
ma-255	497	6	boston	GPE
ma-255	497	7	1984.[26	CARDINAL
ma-255	497	8	a. padcharoen	PERSON
ma-255	497	9	p. kumam	PERSON
ma-255	497	10	p. chaipunya	PERSON
ma-255	497	11	thai	NORP
ma-255	498	1	18	CARDINAL
ma-255	498	2	2020	DATE
ma-255	498	3	126-142.[27	CARDINAL
ma-255	498	4	p.d. proinov	PERSON
ma-255	498	5	newton	GPE
ma-255	498	6	j. complex	PERSON
ma-255	499	1	25 (2010	DATE
ma-255	499	2	3-42.[28	CARDINAL
ma-255	499	3	j. sun	PERSON
ma-255	499	4	newton	ORG
ma-255	500	1	58	CARDINAL
ma-255	500	2	1993	DATE
ma-255	501	1	353	CARDINAL
ma-255	501	2	robinson	PERSON
ma-255	501	3	newton	GPE
ma-255	502	1	19	CARDINAL
ma-255	502	2	rheinboldt	GPE
ma-255	502	3	j. numer	PERSON
ma-255	504	1	5	CARDINAL
ma-255	504	2	1968	DATE
ma-255	504	3	42-63.[31	CARDINAL
ma-255	504	4	i.k. argyros	GPE
ma-255	504	5	s. george	PERSON
ma-255	504	6	c.i.	GPE
ma-255	504	7	three	CARDINAL
ma-255	504	8	14	CARDINAL
ma-255	504	9	2022	CARDINAL
ma-255	505	1	g.n. silva	PERSON
ma-255	505	2	kantorovich	PERSON
ma-255	505	3	newton	GPE
ma-255	505	4	condi-tion	PERSON
ma-255	506	1	comput	PERSON
ma-255	507	1	286	CARDINAL
ma-255	507	2	2016	CARDINAL
ma-255	507	3	178	CARDINAL
ma-255	507	4	h. wozniakowsi	PERSON
ma-255	507	5	newton	GPE
ma-255	507	6	j. assoc.	PERSON
ma-255	509	1	26	CARDINAL
ma-255	509	2	250	CARDINAL
ma-255	509	3	t. yamamoto	PERSON
ma-255	509	4	newton	GPE
ma-255	509	5	numer	ORG
ma-255	510	1	51	CARDINAL
ma-255	510	2	1987	DATE
ma-255	510	3	545	CARDINAL
ma-255	510	4	m. ulbrich	PERSON
ma-255	510	5	newton	GPE
ma-255	510	6	siam	GPE
ma-255	510	7	philadelphia	GPE
ma-255	510	8	2011	DATE
ma-255	511	1	1	CARDINAL
ma-255	511	2	2	CARDINAL
ma-255	511	3	1.5	CARDINAL
ma-255	511	4	3	CARDINAL
ma-255	511	5	1.10	CARDINAL
ma-255	511	6	4	CARDINAL
ma-255	511	7	5	CARDINAL