id	sid	eid	entity	type
ejpam-6256	1	1	european journal	ORG
ejpam-6256	1	2	2025	DATE
ejpam-6256	1	3	18	CARDINAL
ejpam-6256	1	4	3	CARDINAL
ejpam-6256	1	5	6256	CARDINAL
ejpam-6256	2	1	new york	GPE
ejpam-6256	2	2	yassin	PERSON
ejpam-6256	2	3	al-qura university	ORG
ejpam-6256	2	4	saudi arabia	GPE
ejpam-6256	5	1	generalized mp-metric	PERSON
ejpam-6256	7	1	2020	DATE
ejpam-6256	7	2	47h10	CARDINAL
ejpam-6256	9	1	1	CARDINAL
ejpam-6256	9	2	2	CARDINAL
ejpam-6256	10	1	the late 19th	DATE
ejpam-6256	10	2	early 20th centuries	DATE
ejpam-6256	10	3	lefschetz	PERSON
ejpam-6256	10	4	3	CARDINAL
ejpam-6256	11	1	1922	DATE
ejpam-6256	12	1	4	CARDINAL
ejpam-6256	15	1	two	CARDINAL
ejpam-6256	15	2	first	ORDINAL
ejpam-6256	15	3	second	ORDINAL
ejpam-6256	15	4	more than one	CARDINAL
ejpam-6256	16	1	two	CARDINAL
ejpam-6256	17	1	yazubaidi@uqu.edu.sa	PERSON
ejpam-6256	18	1	1	CARDINAL
ejpam-6256	18	2	2025	CARDINAL
ejpam-6256	20	1	j. pure	PERSON
ejpam-6256	20	2	18	CARDINAL
ejpam-6256	20	3	3	CARDINAL
ejpam-6256	20	4	2025	CARDINAL
ejpam-6256	20	5	6256 2	CARDINAL
ejpam-6256	20	6	11	CARDINAL
ejpam-6256	23	1	mann	ORG
ejpam-6256	24	1	5	CARDINAL
ejpam-6256	24	2	6	CARDINAL
ejpam-6256	24	3	8	CARDINAL
ejpam-6256	24	4	9	CARDINAL
ejpam-6256	25	1	the 1960s	DATE
ejpam-6256	25	2	browder	PERSON
ejpam-6256	25	3	kirk	PERSON
ejpam-6256	26	1	10	CARDINAL
ejpam-6256	27	1	11	CARDINAL
ejpam-6256	27	2	12	CARDINAL
ejpam-6256	27	3	13	CARDINAL
ejpam-6256	28	1	more than one	CARDINAL
ejpam-6256	30	1	14	CARDINAL
ejpam-6256	30	2	15	CARDINAL
ejpam-6256	32	1	more than one	CARDINAL
ejpam-6256	39	1	2	CARDINAL
ejpam-6256	40	1	16],[17	CARDINAL
ejpam-6256	40	2	18	CARDINAL
ejpam-6256	40	3	19	CARDINAL
ejpam-6256	40	4	20	CARDINAL
ejpam-6256	42	1	j. pure	PERSON
ejpam-6256	42	2	18	CARDINAL
ejpam-6256	42	3	3	CARDINAL
ejpam-6256	42	4	2025	CARDINAL
ejpam-6256	42	5	6256 3	DATE
ejpam-6256	43	1	1	CARDINAL
ejpam-6256	43	2	21	CARDINAL
ejpam-6256	44	1	x.	GPE
ejpam-6256	45	1	⊆	CARDINAL
ejpam-6256	45	2	•	CARDINAL
ejpam-6256	47	1	•	CARDINAL
ejpam-6256	48	1	d(a	GPE
ejpam-6256	50	1	d(a1	GPE
ejpam-6256	50	2	d(a	GPE
ejpam-6256	51	1	d(2	PERSON
ejpam-6256	52	1	21	CARDINAL
ejpam-6256	54	1	1	CARDINAL
ejpam-6256	54	2	21	CARDINAL
ejpam-6256	57	1	two	CARDINAL
ejpam-6256	62	1	2	CARDINAL
ejpam-6256	62	2	21	CARDINAL
ejpam-6256	63	1	∈	ORG
ejpam-6256	64	1	d(a	GPE
ejpam-6256	64	2	a.	PERSON
ejpam-6256	64	3	2	CARDINAL
ejpam-6256	64	4	21	CARDINAL
ejpam-6256	65	1	example 1	DATE
ejpam-6256	74	1	j. pure	PERSON
ejpam-6256	74	2	18	CARDINAL
ejpam-6256	74	3	3	CARDINAL
ejpam-6256	74	4	2025	CARDINAL
ejpam-6256	74	5	6256 4	DATE
ejpam-6256	74	6	3	CARDINAL
ejpam-6256	74	7	21	CARDINAL
ejpam-6256	76	1	∈	ORG
ejpam-6256	76	2	∪a	CARDINAL
ejpam-6256	77	1	tod(a	GPE
ejpam-6256	79	1	1	CARDINAL
ejpam-6256	79	2	21	CARDINAL
ejpam-6256	80	1	d(2	PERSON
ejpam-6256	81	1	d(2	PERSON
ejpam-6256	85	1	2	CARDINAL
ejpam-6256	85	2	21	CARDINAL
ejpam-6256	86	1	d(2	PERSON
ejpam-6256	87	1	lim	PERSON
ejpam-6256	89	1	1	CARDINAL
ejpam-6256	89	2	lim ni−→∞	PERSON
ejpam-6256	93	1	4	CARDINAL
ejpam-6256	93	2	21	CARDINAL
ejpam-6256	95	1	n ∈ n	ORG
ejpam-6256	95	2	lim m−→∞ sup	PERSON
ejpam-6256	97	1	1	CARDINAL
ejpam-6256	97	2	21	CARDINAL
ejpam-6256	99	1	∈	ORG
ejpam-6256	100	1	3	CARDINAL
ejpam-6256	100	2	21	CARDINAL
ejpam-6256	105	1	j. pure	PERSON
ejpam-6256	105	2	18	CARDINAL
ejpam-6256	105	3	3	CARDINAL
ejpam-6256	105	4	2025	CARDINAL
ejpam-6256	105	5	6256 5	DATE
ejpam-6256	105	6	5	CARDINAL
ejpam-6256	106	1	∈	ORG
ejpam-6256	107	1	d(a	GPE
ejpam-6256	109	1	example 1	DATE
ejpam-6256	110	1	21	CARDINAL
ejpam-6256	111	1	2	CARDINAL
ejpam-6256	111	2	21	CARDINAL
ejpam-6256	113	1	1	CARDINAL
ejpam-6256	114	1	0	CARDINAL
ejpam-6256	115	1	∈	ORG
ejpam-6256	118	1	6	CARDINAL
ejpam-6256	119	1	∈	ORG
ejpam-6256	120	1	3	CARDINAL
ejpam-6256	122	1	∈	ORG
ejpam-6256	125	1	0	CARDINAL
ejpam-6256	125	2	1	CARDINAL
ejpam-6256	125	3	0	CARDINAL
ejpam-6256	125	4	1 ≤ l ≤	QUANTITY
ejpam-6256	126	1	t j−1({al	GPE
ejpam-6256	126	2	2	CARDINAL
ejpam-6256	127	1	4	CARDINAL
ejpam-6256	131	1	t (	ORG
ejpam-6256	131	2	0	CARDINAL
ejpam-6256	132	1	j. pure	PERSON
ejpam-6256	132	2	18	CARDINAL
ejpam-6256	132	3	3	CARDINAL
ejpam-6256	132	4	2025	CARDINAL
ejpam-6256	132	5	6256 6	CARDINAL
ejpam-6256	133	1	sj+1,l	DATE
ejpam-6256	133	2	t	PERSON
ejpam-6256	136	1	⊆	CARDINAL
ejpam-6256	136	2	sj2	PRODUCT
ejpam-6256	136	3	j2 ∈ n	ORG
ejpam-6256	136	4	0	CARDINAL
ejpam-6256	136	5	j2 ≤ j1	ORG
ejpam-6256	136	6	⊆	CARDINAL
ejpam-6256	136	7	1 ≤	QUANTITY
ejpam-6256	136	8	vi	PERSON
ejpam-6256	136	9	⊆	CARDINAL
ejpam-6256	136	10	j2 ∈ n	ORG
ejpam-6256	136	11	1 ≤	QUANTITY
ejpam-6256	136	12	j2 ≤ j1	ORG
ejpam-6256	137	1	7	CARDINAL
ejpam-6256	139	1	t j(a	GPE
ejpam-6256	140	1	t j+1−1({a1	GPE
ejpam-6256	142	1	{a1	PERSON
ejpam-6256	142	2	t 2(a1	DATE
ejpam-6256	143	1	8	DATE
ejpam-6256	145	1	0	CARDINAL
ejpam-6256	146	1	t j(an−jk	GPE
ejpam-6256	146	2	3	CARDINAL
ejpam-6256	147	1	j = int(n−1 k	PERSON
ejpam-6256	151	1	1)k	DATE
ejpam-6256	153	1	∈	ORG
ejpam-6256	154	1	t(ar	GPE
ejpam-6256	154	2	1 ≤	QUANTITY
ejpam-6256	154	3	t s−1(ar	PERSON
ejpam-6256	154	4	∈	ORG
ejpam-6256	155	1	first	ORDINAL
ejpam-6256	156	1	+ tk ≥ l	PERSON
ejpam-6256	157	1	1)k	CARDINAL
ejpam-6256	157	2	second	ORDINAL
ejpam-6256	157	3	1)k ≥ l	DATE
ejpam-6256	158	1	1)k	CARDINAL
ejpam-6256	158	2	m. hence	PERSON
ejpam-6256	160	1	j. pure	PERSON
ejpam-6256	160	2	18	CARDINAL
ejpam-6256	160	3	3	CARDINAL
ejpam-6256	160	4	2025	CARDINAL
ejpam-6256	160	5	6256 7	DATE
ejpam-6256	160	6	1 +	CARDINAL
ejpam-6256	163	1	⊆	CARDINAL
ejpam-6256	165	1	1)k	CARDINAL
ejpam-6256	165	2	⊆	CARDINAL
ejpam-6256	166	1	4-(iii	CARDINAL
ejpam-6256	167	1	6	CARDINAL
ejpam-6256	170	1	sv ∈ n	ORG
ejpam-6256	170	2	sv(a	GPE
ejpam-6256	173	1	∈	ORG
ejpam-6256	173	2	s.t ∀	PERSON
ejpam-6256	173	3	∈	ORG
ejpam-6256	173	4	s.t.	PERSON
ejpam-6256	174	1	∈	ORG
ejpam-6256	174	2	∃	ORG
ejpam-6256	174	3	t sv(ai	ORG
ejpam-6256	175	1	max	PERSON
ejpam-6256	176	1	∈	ORG
ejpam-6256	177	1	t j(an−jk	GPE
ejpam-6256	177	2	8	DATE
ejpam-6256	177	3	3	CARDINAL
ejpam-6256	179	1	3	CARDINAL
ejpam-6256	181	1	n ∈ n	ORG
ejpam-6256	181	2	xu	PERSON
ejpam-6256	181	3	xu}	PERSON
ejpam-6256	182	1	4	CARDINAL
ejpam-6256	182	2	∈	ORG
ejpam-6256	182	3	at least two	CARDINAL
ejpam-6256	183	1	proof	PERSON
ejpam-6256	184	1	4	CARDINAL
ejpam-6256	184	2	int(n−1 k	PERSON
ejpam-6256	184	3	3	CARDINAL
ejpam-6256	186	1	xu	PERSON
ejpam-6256	187	1	xu	PERSON
ejpam-6256	187	2	4-(ii	CARDINAL
ejpam-6256	188	1	5	CARDINAL
ejpam-6256	189	1	j. pure	PERSON
ejpam-6256	189	2	18	CARDINAL
ejpam-6256	189	3	3	CARDINAL
ejpam-6256	189	4	2025	CARDINAL
ejpam-6256	189	5	6256 8	DATE
ejpam-6256	189	6	4	CARDINAL
ejpam-6256	190	1	xu	PERSON
ejpam-6256	191	1	xu}	PERSON
ejpam-6256	194	1	xu	PERSON
ejpam-6256	195	1	≤ q[q	PERSON
ejpam-6256	195	2	xu}	PERSON
ejpam-6256	197	1	xu}	PERSON
ejpam-6256	199	1	xu	PERSON
ejpam-6256	201	1	6	CARDINAL
ejpam-6256	201	2	xu	PERSON
ejpam-6256	203	1	xu}	PERSON
ejpam-6256	204	1	xu}	PERSON
ejpam-6256	205	1	7	CARDINAL
ejpam-6256	206	1	4	CARDINAL
ejpam-6256	206	2	5	CARDINAL
ejpam-6256	206	3	7	CARDINAL
ejpam-6256	207	1	xu}	PERSON
ejpam-6256	208	1	lim	PERSON
ejpam-6256	208	2	m→∞	CARDINAL
ejpam-6256	209	1	9	CARDINAL
ejpam-6256	210	1	10	CARDINAL
ejpam-6256	210	2	lim	PERSON
ejpam-6256	210	3	n→∞ d(αn	GPE
ejpam-6256	210	4	∈	ORG
ejpam-6256	210	5	3	CARDINAL
ejpam-6256	212	1	lim nm→∞ d(αnm	PERSON
ejpam-6256	212	2	0	CARDINAL
ejpam-6256	213	1	∈	ORG
ejpam-6256	215	1	0	CARDINAL
ejpam-6256	216	1	sl→∞ d(t sl(a	PERSON
ejpam-6256	217	1	sl→∞ d(t	PERSON
ejpam-6256	217	2	lim sl→∞	PERSON
ejpam-6256	218	1	j. pure	PERSON
ejpam-6256	218	2	18	CARDINAL
ejpam-6256	218	3	3	CARDINAL
ejpam-6256	218	4	2025	CARDINAL
ejpam-6256	218	5	6256 9 of 11	DATE
ejpam-6256	222	1	11	CARDINAL
ejpam-6256	222	2	m→∞	CARDINAL
ejpam-6256	222	3	12	CARDINAL
ejpam-6256	222	4	10	CARDINAL
ejpam-6256	222	5	3	CARDINAL
ejpam-6256	222	6	lim ni→∞	PERSON
ejpam-6256	223	1	lim	PERSON
ejpam-6256	223	2	m→∞	CARDINAL
ejpam-6256	223	3	lim	PERSON
ejpam-6256	223	4	m→∞	CARDINAL
ejpam-6256	224	1	lim ni→∞	PERSON
ejpam-6256	224	2	13	CARDINAL
ejpam-6256	224	3	12	CARDINAL
ejpam-6256	224	4	13	CARDINAL
ejpam-6256	225	1	14	CARDINAL
ejpam-6256	226	1	at least two	CARDINAL
ejpam-6256	228	1	3	CARDINAL
ejpam-6256	229	1	1	CARDINAL
ejpam-6256	230	1	max(a)− min(a	PERSON
ejpam-6256	231	1	0	CARDINAL
ejpam-6256	231	2	1	CARDINAL
ejpam-6256	232	1	0	CARDINAL
ejpam-6256	233	1	0	CARDINAL
ejpam-6256	233	2	1	CARDINAL
ejpam-6256	234	1	0	CARDINAL
ejpam-6256	234	2	1	CARDINAL
ejpam-6256	236	1	0	CARDINAL
ejpam-6256	236	2	1	CARDINAL
ejpam-6256	236	3	0	CARDINAL
ejpam-6256	236	4	1	CARDINAL
ejpam-6256	237	1	1	CARDINAL
ejpam-6256	237	2	1 2	CARDINAL
ejpam-6256	237	3	1	CARDINAL
ejpam-6256	237	4	1 2	CARDINAL
ejpam-6256	237	5	1	DATE
ejpam-6256	237	6	1 2	CARDINAL
ejpam-6256	237	7	1	CARDINAL
ejpam-6256	237	8	12	CARDINAL
ejpam-6256	237	9	1	CARDINAL
ejpam-6256	238	1	1	CARDINAL
ejpam-6256	238	2	2	CARDINAL
ejpam-6256	238	3	1−	TIME
ejpam-6256	238	4	0	CARDINAL
ejpam-6256	238	5	1	CARDINAL
ejpam-6256	238	6	1 ≤	QUANTITY
ejpam-6256	238	7	xu	PERSON
ejpam-6256	239	1	xu}	PERSON
ejpam-6256	240	1	1−	TIME
ejpam-6256	240	2	2	CARDINAL
ejpam-6256	241	1	0	CARDINAL
ejpam-6256	241	2	1	CARDINAL
ejpam-6256	241	3	3	CARDINAL
ejpam-6256	242	1	1	CARDINAL
ejpam-6256	243	1	0	CARDINAL
ejpam-6256	243	2	1	CARDINAL
ejpam-6256	244	1	lim	PERSON
ejpam-6256	244	2	n→∞	CARDINAL
ejpam-6256	244	3	0	CARDINAL
ejpam-6256	244	4	lim	ORG
ejpam-6256	244	5	n→∞	CARDINAL
ejpam-6256	245	1	1	CARDINAL
ejpam-6256	245	2	4	CARDINAL
ejpam-6256	246	1	generalized mp-metric	PERSON
ejpam-6256	247	1	j. pure	PERSON
ejpam-6256	247	2	18	CARDINAL
ejpam-6256	247	3	3	CARDINAL
ejpam-6256	247	4	2025	CARDINAL
ejpam-6256	247	5	6256 10	DATE
ejpam-6256	249	1	research.for	NORP
ejpam-6256	249	2	δ(f1	ORG
ejpam-6256	249	3	f2	ORG
ejpam-6256	251	1	two	CARDINAL
ejpam-6256	252	1	c[a	PERSON
ejpam-6256	257	1	22	CARDINAL
ejpam-6256	257	2	23	CARDINAL
ejpam-6256	259	1	al-qura university	ORG
ejpam-6256	259	2	saudi arabia	GPE
ejpam-6256	259	3	25uqu4230209gssr01	CARDINAL
ejpam-6256	259	4	1	CARDINAL
ejpam-6256	259	5	p. k.	PERSON
ejpam-6256	262	1	international journal of statistics	ORG
ejpam-6256	262	2	2(5):25–34	CARDINAL
ejpam-6256	262	3	2017	DATE
ejpam-6256	263	1	2	CARDINAL
ejpam-6256	263	2	f. kamalov	PERSON
ejpam-6256	263	3	h. h. leung	PERSON
ejpam-6256	265	1	2023	CARDINAL
ejpam-6256	266	1	3	CARDINAL
ejpam-6256	266	2	a. granas	PERSON
ejpam-6256	266	3	j. dugundji	PERSON
ejpam-6256	268	1	new york	GPE
ejpam-6256	268	2	2003	DATE
ejpam-6256	269	1	4	CARDINAL
ejpam-6256	270	1	sur les opérations dans les	ORG
ejpam-6256	270	2	aux équations	ORG
ejpam-6256	271	1	fundamenta mathematicae	ORG
ejpam-6256	271	2	3:133–181	CARDINAL
ejpam-6256	271	3	1922	DATE
ejpam-6256	272	1	5	CARDINAL
ejpam-6256	272	2	gazal	PERSON
ejpam-6256	272	3	s. rathee	PERSON
ejpam-6256	272	4	mahima	PERSON
ejpam-6256	272	5	a. kadyan	PERSON
ejpam-6256	272	6	minakshi	ORG
ejpam-6256	272	7	a. kumar	PERSON
ejpam-6256	273	1	ćirić	ORG
ejpam-6256	274	1	12(7	CARDINAL
ejpam-6256	274	2	2023	CARDINAL
ejpam-6256	275	1	6	CARDINAL
ejpam-6256	277	1	london	GPE
ejpam-6256	277	2	2007	DATE
ejpam-6256	279	1	j. pure	PERSON
ejpam-6256	279	2	18	CARDINAL
ejpam-6256	279	3	3	CARDINAL
ejpam-6256	279	4	2025	CARDINAL
ejpam-6256	279	5	6256 11	DATE
ejpam-6256	280	1	7	CARDINAL
ejpam-6256	280	2	j. ahmad	PERSON
ejpam-6256	280	3	k. ullah	PERSON
ejpam-6256	280	4	m. arshad	PERSON
ejpam-6256	280	5	m. de la	PERSON
ejpam-6256	281	1	2021(1	CARDINAL
ejpam-6256	281	2	2021	CARDINAL
ejpam-6256	282	1	8	CARDINAL
ejpam-6256	282	2	m. r. haddadi	PERSON
ejpam-6256	282	3	m. bota	PERSON
ejpam-6256	284	1	8(5):12185–12194	DATE
ejpam-6256	284	2	2023	CARDINAL
ejpam-6256	285	1	9	CARDINAL
ejpam-6256	285	2	t. a. burton	PERSON
ejpam-6256	287	1	1998	DATE
ejpam-6256	288	1	10	CARDINAL
ejpam-6256	288	2	f. e. browder	PERSON
ejpam-6256	290	1	american	NORP
ejpam-6256	290	2	16:638–640	CARDINAL
ejpam-6256	290	3	1965	DATE
ejpam-6256	291	1	11	CARDINAL
ejpam-6256	291	2	f. e. browder	PERSON
ejpam-6256	293	1	15(3):517–528, 1967	DATE
ejpam-6256	294	1	12	CARDINAL
ejpam-6256	294	2	w. a. kirk	PERSON
ejpam-6256	296	1	american	NORP
ejpam-6256	296	2	monthly	DATE
ejpam-6256	296	3	72(9):1004–1006	CARDINAL
ejpam-6256	296	4	1965	DATE
ejpam-6256	297	1	13	CARDINAL
ejpam-6256	297	2	w. a. kirk	PERSON
ejpam-6256	298	1	nonexpansive	PERSON
ejpam-6256	299	1	illinois journal of mathematics	ORG
ejpam-6256	299	2	11(3):474–479	ORG
ejpam-6256	299	3	1967	DATE
ejpam-6256	300	1	14	CARDINAL
ejpam-6256	300	2	h. persson	PERSON
ejpam-6256	302	1	2006	DATE
ejpam-6256	303	1	15	CARDINAL
ejpam-6256	303	2	e. n.	PERSON
ejpam-6256	305	1	und angewandte mathematik	PERSON
ejpam-6256	305	2	1986(371):46–66, 1986	DATE
ejpam-6256	306	1	16	CARDINAL
ejpam-6256	306	2	r. p. agarwal	PERSON
ejpam-6256	306	3	e. karapınar	GPE
ejpam-6256	306	4	d. o’regan	PERSON
ejpam-6256	306	5	a. f. roldán-lópez-de	PERSON
ejpam-6256	307	1	springer, cham	ORG
ejpam-6256	307	2	switzerland	GPE
ejpam-6256	307	3	2015	DATE
ejpam-6256	308	1	17	CARDINAL
ejpam-6256	308	2	d. gopal	PERSON
ejpam-6256	308	3	p. agarwal	PERSON
ejpam-6256	308	4	p. kumam	PERSON
ejpam-6256	310	1	crc press	ORG
ejpam-6256	310	2	2021	CARDINAL
ejpam-6256	311	1	18	CARDINAL
ejpam-6256	311	2	r. p. agarwal	PERSON
ejpam-6256	313	1	2022	CARDINAL
ejpam-6256	314	1	19	CARDINAL
ejpam-6256	314	2	s. anwar	PERSON
ejpam-6256	314	3	m. nazam	PERSON
ejpam-6256	314	4	h. h. al sulami	PERSON
ejpam-6256	314	5	a. hussain	PERSON
ejpam-6256	314	6	k. javed	PERSON
ejpam-6256	314	7	m. arshad	PERSON
ejpam-6256	316	1	7(5):8188–8205	DATE
ejpam-6256	316	2	2022	CARDINAL
ejpam-6256	317	1	20	CARDINAL
ejpam-6256	319	1	6(4):610–621, 2008	DATE
ejpam-6256	320	1	21	CARDINAL
ejpam-6256	322	1	asia pacific journal of mathematics	ORG
ejpam-6256	322	2	11(11	CARDINAL
ejpam-6256	322	3	2024	DATE
ejpam-6256	323	1	22	CARDINAL
ejpam-6256	323	2	nabil mlaiki	PERSON
ejpam-6256	323	3	nihal	ORG
ejpam-6256	324	1	filomat	ORG
ejpam-6256	324	2	35(2):447–457	ORG
ejpam-6256	324	3	2021	DATE
ejpam-6256	325	1	23	CARDINAL
ejpam-6256	325	2	aftab hussain	PERSON
ejpam-6256	325	3	hamed al-sulami	PERSON
ejpam-6256	325	4	nawab hussain	PERSON
ejpam-6256	325	5	hamza farooq	PERSON
ejpam-6256	327	1	10(6):2313–2322	CARDINAL
ejpam-6256	327	2	2020	DATE