id	sid	eid	entity	type
iajs-2952	1	1	ihjpas	PERSON
iajs-2952	2	1	36(1)2023 311	CARDINAL
iajs-2952	2	2	4.0	CARDINAL
iajs-2952	2	3	2	CARDINAL
iajs-2952	3	1	kreyszig	PERSON
iajs-2952	4	1	2	CARDINAL
iajs-2952	5	1	ŵ	PERSON
iajs-2952	7	1	2	CARDINAL
iajs-2952	8	1	1	CARDINAL
iajs-2952	8	2	3	CARDINAL
iajs-2952	8	3	2	CARDINAL
iajs-2952	8	4	w × w	PRODUCT
iajs-2952	8	5	w	GPE
iajs-2952	8	6	∈	ORG
iajs-2952	8	7	1	CARDINAL
iajs-2952	8	8	‖w	DATE
iajs-2952	9	1	w	ORG
iajs-2952	10	1	2	CARDINAL
iajs-2952	10	2	‖w	DATE
iajs-2952	11	1	3	CARDINAL
iajs-2952	12	1	4	CARDINAL
iajs-2952	13	1	z‖ +	DATE
iajs-2952	13	2	z‖	CARDINAL
iajs-2952	13	3	2	CARDINAL
iajs-2952	13	4	2	CARDINAL
iajs-2952	13	5	2	CARDINAL
iajs-2952	14	1	11-12	CARDINAL
iajs-2952	14	2	14	CARDINAL
iajs-2952	14	3	2022	CARDINAL
iajs-2952	14	4	11	CARDINAL
iajs-2952	14	5	january 2023	DATE
iajs-2952	15	1	ibn al-haitham	PERSON
iajs-2952	15	2	applied sciences journal	ORG
iajs-2952	15	3	jih.uobaghdad.edu.iq safa l. hamad	PERSON
iajs-2952	15	4	university of baghdadiraq	ORG
iajs-2952	16	1	zeana z. jamil	PERSON
iajs-2952	16	2	university of baghdadiraq	ORG
iajs-2952	17	1	https://creativecommons.org/licenses/by/4.0/	LANGUAGE
iajs-2952	18	1	mailto:safalafta2019@gmail.com	NORP
iajs-2952	18	2	mailto:zina.z@sc.uobaghdad.edu.iq ihjpas	PERSON
iajs-2952	19	1	36(1)2023 312	CARDINAL
iajs-2952	19	2	10	CARDINAL
iajs-2952	19	3	2	CARDINAL
iajs-2952	19	4	2	CARDINAL
iajs-2952	20	1	1	CARDINAL
iajs-2952	21	1	2	CARDINAL
iajs-2952	22	1	w	GPE
iajs-2952	22	2	0	CARDINAL
iajs-2952	23	1	3	CARDINAL
iajs-2952	25	1	4.	CARDINAL
iajs-2952	29	1	6	CARDINAL
iajs-2952	29	2	2	CARDINAL
iajs-2952	29	3	2	CARDINAL
iajs-2952	29	4	1 2	DATE
iajs-2952	30	1	2	CARDINAL
iajs-2952	30	2	2014	DATE
iajs-2952	30	3	10	CARDINAL
iajs-2952	30	4	2	CARDINAL
iajs-2952	30	5	w × w	PRODUCT
iajs-2952	30	6	w.	PERSON
iajs-2952	30	7	2	CARDINAL
iajs-2952	32	1	kreyszig	PERSON
iajs-2952	32	2	1978	DATE
iajs-2952	33	1	2001	DATE
iajs-2952	34	1	3	CARDINAL
iajs-2952	34	2	2normed	CARDINAL
iajs-2952	35	1	2	CARDINAL
iajs-2952	35	2	2	CARDINAL
iajs-2952	35	3	2	CARDINAL
iajs-2952	36	1	two	CARDINAL
iajs-2952	37	1	first	ORDINAL
iajs-2952	37	2	2	CARDINAL
iajs-2952	38	1	second	ORDINAL
iajs-2952	38	2	2	CARDINAL
iajs-2952	39	1	‖w	DATE
iajs-2952	40	1	2	CARDINAL
iajs-2952	41	1	2inner	PRODUCT
iajs-2952	42	1	mazaheri	NORP
iajs-2952	42	2	kazemi	PERSON
iajs-2952	42	3	9	CARDINAL
iajs-2952	42	4	2	CARDINAL
iajs-2952	42	5	lim 𝑛,𝑚→∞	PERSON
iajs-2952	44	1	9	CARDINAL
iajs-2952	44	2	2.2	CARDINAL
iajs-2952	44	3	2	CARDINAL
iajs-2952	44	4	‖w	DATE
iajs-2952	46	1	2inner	PRODUCT
iajs-2952	47	1	first	ORDINAL
iajs-2952	47	2	0	CARDINAL
iajs-2952	48	1	2.3	CARDINAL
iajs-2952	48	2	w	ORG
iajs-2952	48	3	2	CARDINAL
iajs-2952	48	4	0	CARDINAL
iajs-2952	48	5	w ∈	ORG
iajs-2952	49	1	⊂	GPE
iajs-2952	50	1	36(1)2023 313	CARDINAL
iajs-2952	50	2	2.4	CARDINAL
iajs-2952	50	3	2	CARDINAL
iajs-2952	50	4	w	GPE
iajs-2952	51	1	0	CARDINAL
iajs-2952	51	2	≥ m(u	PERSON
iajs-2952	51	3	0	CARDINAL
iajs-2952	51	4	0	CARDINAL
iajs-2952	51	5	⊆	CARDINAL
iajs-2952	51	6	w	GPE
iajs-2952	51	7	0	CARDINAL
iajs-2952	52	1	m(ε	PERSON
iajs-2952	52	2	0	CARDINAL
iajs-2952	53	1	− wm	PERSON
iajs-2952	53	2	⊆	CARDINAL
iajs-2952	53	3	w	GPE
iajs-2952	53	4	0	CARDINAL
iajs-2952	53	5	0	CARDINAL
iajs-2952	53	6	− wm	PERSON
iajs-2952	53	7	≥ m(u	PERSON
iajs-2952	54	1	δ(u	ORG
iajs-2952	54	2	0	CARDINAL
iajs-2952	55	1	≥ m(u	PERSON
iajs-2952	56	1	0	CARDINAL
iajs-2952	56	2	m(ε	PERSON
iajs-2952	56	3	0	CARDINAL
iajs-2952	57	1	w.∎ 3	ORG
iajs-2952	57	2	2	CARDINAL
iajs-2952	58	1	kreyszig	PERSON
iajs-2952	59	1	1	CARDINAL
iajs-2952	60	1	2	CARDINAL
iajs-2952	61	1	step1	GPE
iajs-2952	62	1	3.1	CARDINAL
iajs-2952	62	2	two	CARDINAL
iajs-2952	62	3	2	CARDINAL
iajs-2952	62	4	0	CARDINAL
iajs-2952	65	1	3.2	CARDINAL
iajs-2952	65	2	w	GPE
iajs-2952	65	3	w. proof	PERSON
iajs-2952	66	1	0	CARDINAL
iajs-2952	67	1	0	CARDINAL
iajs-2952	67	2	2.1	CARDINAL
iajs-2952	68	1	u for n ≥ m. therefore	ORG
iajs-2952	68	2	ŵ	PERSON
iajs-2952	68	3	ŵ	PERSON
iajs-2952	68	4	ŵ	PERSON
iajs-2952	69	1	2	CARDINAL
iajs-2952	71	1	•	CARDINAL
iajs-2952	72	1	36(1)2023 314	CARDINAL
iajs-2952	72	2	two	CARDINAL
iajs-2952	73	1	first	ORDINAL
iajs-2952	73	2	3.3	CARDINAL
iajs-2952	73	3	2	CARDINAL
iajs-2952	75	1	lim n→∞	LAW
iajs-2952	76	1	zero	CARDINAL
iajs-2952	76	2	m(u	PERSON
iajs-2952	76	3	0	CARDINAL
iajs-2952	76	4	∈	ORG
iajs-2952	77	1	0	CARDINAL
iajs-2952	77	2	0	CARDINAL
iajs-2952	79	1	m(δ	PERSON
iajs-2952	79	2	0	CARDINAL
iajs-2952	80	1	lim n→∞	PERSON
iajs-2952	81	1	w	GPE
iajs-2952	81	2	0	CARDINAL
iajs-2952	81	3	0	CARDINAL
iajs-2952	82	1	lim	PERSON
iajs-2952	82	2	n→∞	CARDINAL
iajs-2952	83	1	m(ε	PERSON
iajs-2952	83	2	0	CARDINAL
iajs-2952	85	1	∈	PRODUCT
iajs-2952	85	2	3.4	CARDINAL
iajs-2952	85	3	2	CARDINAL
iajs-2952	85	4	w.	PERSON
iajs-2952	89	1	− bn‖b	PERSON
iajs-2952	90	1	0	CARDINAL
iajs-2952	90	2	lim	PERSON
iajs-2952	90	3	0	CARDINAL
iajs-2952	91	1	2	CARDINAL
iajs-2952	92	1	1	CARDINAL
iajs-2952	92	2	2	CARDINAL
iajs-2952	92	3	2.3	CARDINAL
iajs-2952	92	4	ŵ	PERSON
iajs-2952	92	5	step3	LOC
iajs-2952	92	6	2	CARDINAL
iajs-2952	93	1	2	CARDINAL
iajs-2952	95	1	3.5	CARDINAL
iajs-2952	95	2	w	ORG
iajs-2952	95	3	2	CARDINAL
iajs-2952	95	4	two	CARDINAL
iajs-2952	95	5	w	GPE
iajs-2952	95	6	ihjpas	PERSON
iajs-2952	96	1	36(1)2023	CARDINAL
iajs-2952	97	1	lim	PERSON
iajs-2952	98	1	2.	CARDINAL
iajs-2952	98	2	lim	PERSON
iajs-2952	98	3	− bn‖b	PERSON
iajs-2952	100	1	1	CARDINAL
iajs-2952	101	1	two	CARDINAL
iajs-2952	102	1	− yn‖b	PERSON
iajs-2952	102	2	− yn‖b	PERSON
iajs-2952	106	1	4	CARDINAL
iajs-2952	106	2	1.1	CARDINAL
iajs-2952	106	3	lim	PERSON
iajs-2952	108	1	r.	NORP
iajs-2952	108	2	lim	PERSON
iajs-2952	109	1	2.	CARDINAL
iajs-2952	110	1	4	CARDINAL
iajs-2952	115	1	− bn‖b	PERSON
iajs-2952	115	2	2.3	CARDINAL
iajs-2952	115	3	lim	PERSON
iajs-2952	118	1	− bn‖b .∎	PERSON
iajs-2952	119	1	3	CARDINAL
iajs-2952	119	2	2.3	CARDINAL
iajs-2952	119	3	1-3	DATE
iajs-2952	119	4	2	CARDINAL
iajs-2952	120	1	3.6	CARDINAL
iajs-2952	120	2	2	CARDINAL
iajs-2952	122	1	− zn‖b	PERSON
iajs-2952	122	2	− ŷ‖b̂ +	PERSON
iajs-2952	122	3	− ẑ‖b̂	PERSON
iajs-2952	122	4	2	CARDINAL
iajs-2952	122	5	step4	PERSON
iajs-2952	123	1	ŵ	PERSON
iajs-2952	124	1	⊂	GPE
iajs-2952	124	2	w	GPE
iajs-2952	124	3	w	GPE
iajs-2952	125	1	one	CARDINAL
iajs-2952	126	1	− ŷ‖b̂	PERSON
iajs-2952	127	1	− y‖b	PERSON
iajs-2952	128	1	ihjpas	PERSON
iajs-2952	129	1	36(1)2023 316	CARDINAL
iajs-2952	129	2	5	CARDINAL
iajs-2952	130	1	3.7	CARDINAL
iajs-2952	130	2	w	ORG
iajs-2952	130	3	2	CARDINAL
iajs-2952	130	4	ŵ ∈	PERSON
iajs-2952	132	1	wm	GPE
iajs-2952	132	2	wm	PERSON
iajs-2952	132	3	∈	ORG
iajs-2952	133	1	1.1	CARDINAL
iajs-2952	134	1	= lim 𝑛,𝑚→∞	PERSON
iajs-2952	134	2	0	CARDINAL
iajs-2952	135	1	6	CARDINAL
iajs-2952	136	1	3.8	CARDINAL
iajs-2952	136	2	w	ORG
iajs-2952	136	3	2	CARDINAL
iajs-2952	137	1	‖ŵn	ORG
iajs-2952	140	1	3	CARDINAL
iajs-2952	140	2	1.1	CARDINAL
iajs-2952	140	3	lim 𝑛,𝑚→∞	PERSON
iajs-2952	142	1	w	PERSON
iajs-2952	143	1	w	GPE
iajs-2952	143	2	‖ŵn	ORG
iajs-2952	144	1	ẑn‖b̂.	GPE
iajs-2952	144	2	lim	PERSON
iajs-2952	144	3	‖ŵn	ORG
iajs-2952	145	1	ŵ	PERSON
iajs-2952	146	1	3.9	CARDINAL
iajs-2952	147	1	ŷ	PERSON
iajs-2952	147	2	ŷ.	GPE
iajs-2952	147	3	4	CARDINAL
iajs-2952	151	1	ŷ	GPE
iajs-2952	151	2	ŷ1n	ORG
iajs-2952	151	3	ŷ1n	ORG
iajs-2952	151	4	ŷ2n	GPE
iajs-2952	152	1	4	CARDINAL
iajs-2952	152	2	1𝑛	CARDINAL
iajs-2952	152	3	2𝑛‖𝑏| ≤	QUANTITY
iajs-2952	152	4	1𝑛‖𝑏	CARDINAL
iajs-2952	152	5	2	CARDINAL
iajs-2952	152	6	2𝑛‖𝑏	CARDINAL
iajs-2952	152	7	0	CARDINAL
iajs-2952	153	1	1𝑛	CARDINAL
iajs-2952	153	2	2𝑛‖𝑏	CARDINAL
iajs-2952	153	3	5	CARDINAL
iajs-2952	153	4	1𝑛	CARDINAL
iajs-2952	153	5	2𝑛‖𝑏	CARDINAL
iajs-2952	153	6	6	CARDINAL
iajs-2952	154	1	36(1)2023 317	CARDINAL
iajs-2952	154	2	5	CARDINAL
iajs-2952	154	3	6	CARDINAL
iajs-2952	154	4	1𝑛	CARDINAL
iajs-2952	154	5	2𝑛‖𝑏	CARDINAL
iajs-2952	154	6	1𝑛	CARDINAL
iajs-2952	154	7	2𝑛‖𝑏	CARDINAL
iajs-2952	154	8	4	CARDINAL
iajs-2952	156	1	w.	PERSON
iajs-2952	156	2	2	CARDINAL
iajs-2952	157	1	1.anshul	CARDINAL
iajs-2952	157	2	r.	NORP
iajs-2952	157	3	k., s.	PERSON
iajs-2952	157	4	sumit	ORG
iajs-2952	157	5	2	CARDINAL
iajs-2952	159	1	2021	CARDINAL
iajs-2952	159	2	17	DATE
iajs-2952	159	3	3	CARDINAL
iajs-2952	159	4	341–368	DATE
iajs-2952	160	1	2.bahram	CARDINAL
iajs-2952	160	2	d.	NORP
iajs-2952	161	1	mohammad	PERSON
iajs-2952	161	2	j.	PERSON
iajs-2952	161	3	2	CARDINAL
iajs-2952	161	4	iranian	NORP
iajs-2952	161	5	2018	DATE
iajs-2952	161	6	13	DATE
iajs-2952	161	7	1	CARDINAL
iajs-2952	161	8	103	CARDINAL
iajs-2952	162	1	3.cho	DATE
iajs-2952	162	2	freese	NORP
iajs-2952	162	3	r. w.	PERSON
iajs-2952	162	4	2	CARDINAL
iajs-2952	162	5	nova science publishers	ORG
iajs-2952	162	6	new york	GPE
iajs-2952	162	7	2001	DATE
iajs-2952	163	1	4.y	CARDINAL
iajs-2952	164	1	j. cho	PERSON
iajs-2952	164	2	m. matic	PERSON
iajs-2952	164	3	j. e.	PERSON
iajs-2952	164	4	2	CARDINAL
iajs-2952	164	5	j. korean	NORP
iajs-2952	165	1	2001	DATE
iajs-2952	165	2	38(4	CARDINAL
iajs-2952	165	3	1125–1156	CARDINAL
iajs-2952	166	1	5.debnath	CARDINAL
iajs-2952	166	2	saha	PERSON
iajs-2952	166	3	m.	PERSON
iajs-2952	167	1	asian	NORP
iajs-2952	168	1	j. math	PERSON
iajs-2952	168	2	2018,11(4	TIME
iajs-2952	168	3	1–10	CARDINAL
iajs-2952	169	1	6.ghafoor	CARDINAL
iajs-2952	169	2	r.	NORP
iajs-2952	169	3	jamil	GPE
iajs-2952	169	4	z., z.	PERSON
iajs-2952	169	5	university of baghdad	ORG
iajs-2952	169	6	baghdad	GPE
iajs-2952	169	7	2018	DATE
iajs-2952	169	8	27	CARDINAL
iajs-2952	170	1	erwin	GPE
iajs-2952	170	2	john wiley	PERSON
iajs-2952	170	3	new york	GPE
iajs-2952	170	4	1978	DATE
iajs-2952	171	1	2	CARDINAL
iajs-2952	172	1	2021	CARDINAL
iajs-2952	172	2	67	DATE
iajs-2952	173	1	9.mazaheri	CARDINAL
iajs-2952	173	2	kazemi	GPE
iajs-2952	173	3	r.	NORP
iajs-2952	173	4	2	CARDINAL
iajs-2952	175	1	2007	DATE
iajs-2952	175	2	37	DATE
iajs-2952	175	3	35	CARDINAL
iajs-2952	176	1	10.riyas	CARDINAL
iajs-2952	176	2	k.	PERSON
iajs-2952	176	3	t.	GPE
iajs-2952	176	4	2	CARDINAL
iajs-2952	176	5	global journal mathematics,	ORG
iajs-2952	176	6	2015	DATE
iajs-2952	176	7	3	CARDINAL
iajs-2952	176	8	1	DATE
iajs-2952	176	9	may 18	DATE
iajs-2952	176	10	244	CARDINAL
iajs-2952	177	1	11.sibel	CARDINAL
iajs-2952	177	2	e. ideal strong	ORG
iajs-2952	177	3	2	CARDINAL
iajs-2952	178	1	aip	ORG
iajs-2952	178	2	2334	CARDINAL
iajs-2952	179	1	12.vijayakumar	DATE
iajs-2952	179	2	s.	PERSON
iajs-2952	179	3	baskaran b.	PERSON
iajs-2952	179	4	2	CARDINAL
iajs-2952	180	1	aip	ORG
iajs-2952	180	2	2282	CARDINAL