id	sid	eid	entity	type
ejpam-3165	1	1	european journal	ORG
ejpam-3165	2	1	11	CARDINAL
ejpam-3165	2	2	1, 2018	DATE
ejpam-3165	2	3	352	CARDINAL
ejpam-3165	2	4	1307-5543	DATE
ejpam-3165	2	5	new york	GPE
ejpam-3165	2	6	e. d. j. owusu-ansah1	PERSON
ejpam-3165	2	7	s. k. amponsah1	PERSON
ejpam-3165	2	8	i. a. adjei1	PERSON
ejpam-3165	3	1	1	CARDINAL
ejpam-3165	3	2	kwame nkrumah university of science and technology	ORG
ejpam-3165	3	3	kumasi	GPE
ejpam-3165	3	4	ghana	GPE
ejpam-3165	4	1	‖v‖	ORG
ejpam-3165	6	1	first	ORDINAL
ejpam-3165	6	2	second	ORDINAL
ejpam-3165	6	3	two	CARDINAL
ejpam-3165	7	1	2010	DATE
ejpam-3165	7	2	44b43	CARDINAL
ejpam-3165	7	3	44b44	CARDINAL
ejpam-3165	7	4	1	CARDINAL
ejpam-3165	8	1	two	CARDINAL
ejpam-3165	10	1	one	CARDINAL
ejpam-3165	11	1	1	CARDINAL
ejpam-3165	11	2	2	CARDINAL
ejpam-3165	12	1	‖v‖	ORG
ejpam-3165	15	1	e. d. j. owusu-ansah	PERSON
ejpam-3165	15	2	skamponsah@knust.edu.gh	DATE
ejpam-3165	15	3	s. k. amponsah	PERSON
ejpam-3165	16	1	352	CARDINAL
ejpam-3165	16	2	2018	DATE
ejpam-3165	17	1	barnes et al	PERSON
ejpam-3165	18	1	j. pure	PERSON
ejpam-3165	18	2	11	CARDINAL
ejpam-3165	18	3	1	CARDINAL
ejpam-3165	18	4	2018	DATE
ejpam-3165	18	5	352	CARDINAL
ejpam-3165	18	6	361 353	CARDINAL
ejpam-3165	18	7	3	CARDINAL
ejpam-3165	19	1	4	CARDINAL
ejpam-3165	19	2	generalized minkowski	PERSON
ejpam-3165	20	1	5	CARDINAL
ejpam-3165	20	2	q−norm	PERSON
ejpam-3165	21	1	6	CARDINAL
ejpam-3165	23	1	8	CARDINAL
ejpam-3165	24	1	9	CARDINAL
ejpam-3165	29	1	xn‖p ≤ ‖x1‖p	PERSON
ejpam-3165	33	1	one	CARDINAL
ejpam-3165	33	2	the 21st century	DATE
ejpam-3165	33	3	‖v‖	ORG
ejpam-3165	33	4	1	CARDINAL
ejpam-3165	33	5	two	CARDINAL
ejpam-3165	34	1	10	CARDINAL
ejpam-3165	36	1	11	CARDINAL
ejpam-3165	37	1	1	CARDINAL
ejpam-3165	37	2	two	CARDINAL
ejpam-3165	41	1	section 1	LAW
ejpam-3165	41	2	1	CARDINAL
ejpam-3165	41	3	section 2	LAW
ejpam-3165	41	4	3	CARDINAL
ejpam-3165	42	1	2	CARDINAL
ejpam-3165	42	2	1	CARDINAL
ejpam-3165	43	1	firstly	ORDINAL
ejpam-3165	43	2	two	CARDINAL
ejpam-3165	43	3	two	CARDINAL
ejpam-3165	45	1	1	CARDINAL
ejpam-3165	47	1	0	CARDINAL
ejpam-3165	50	1	two	CARDINAL
ejpam-3165	50	2	12	CARDINAL
ejpam-3165	51	1	barnes et al	PERSON
ejpam-3165	52	1	j. pure	PERSON
ejpam-3165	52	2	11	CARDINAL
ejpam-3165	52	3	1	CARDINAL
ejpam-3165	52	4	2018	DATE
ejpam-3165	52	5	352	CARDINAL
ejpam-3165	52	6	1	CARDINAL
ejpam-3165	53	1	two	CARDINAL
ejpam-3165	53	2	13	CARDINAL
ejpam-3165	54	1	2.1	CARDINAL
ejpam-3165	56	1	1	CARDINAL
ejpam-3165	57	1	firstly	ORDINAL
ejpam-3165	57	2	2	CARDINAL
ejpam-3165	57	3	0	CARDINAL
ejpam-3165	57	4	u	NORP
ejpam-3165	57	5	+ 2(u	DATE
ejpam-3165	57	6	u	NORP
ejpam-3165	58	1	4(u	CARDINAL
ejpam-3165	58	2	4(u	CARDINAL
ejpam-3165	58	3	2	CARDINAL
ejpam-3165	58	4	u)− 2(u	PERSON
ejpam-3165	58	5	2(u	CARDINAL
ejpam-3165	58	6	u	NORP
ejpam-3165	58	7	4(u	CARDINAL
ejpam-3165	58	8	u	NORP
ejpam-3165	58	9	+ 2(u	DATE
ejpam-3165	58	10	4(u	CARDINAL
ejpam-3165	58	11	v)‖ = ‖(u+ v)2‖	PERSON
ejpam-3165	58	12	4‖u‖‖v‖ ≤	QUANTITY
ejpam-3165	58	13	3	CARDINAL
ejpam-3165	58	14	2	CARDINAL
ejpam-3165	58	15	3	CARDINAL
ejpam-3165	58	16	1 2	CARDINAL
ejpam-3165	58	17	1 2	CARDINAL
ejpam-3165	59	1	‖v‖	ORG
ejpam-3165	59	2	0	CARDINAL
ejpam-3165	60	1	j. pure	PERSON
ejpam-3165	60	2	11	CARDINAL
ejpam-3165	60	3	1	CARDINAL
ejpam-3165	60	4	2018	DATE
ejpam-3165	60	5	352	CARDINAL
ejpam-3165	60	6	u)(u	ORG
ejpam-3165	60	7	+ 6(u	DATE
ejpam-3165	60	8	u)(v	NORP
ejpam-3165	61	1	+ 4(u	CARDINAL
ejpam-3165	62	1	0	CARDINAL
ejpam-3165	62	2	u)(v	NORP
ejpam-3165	62	3	u)(v	NORP
ejpam-3165	62	4	u)(v	NORP
ejpam-3165	62	5	4(u	CARDINAL
ejpam-3165	62	6	u)(u	ORG
ejpam-3165	62	7	4(u	CARDINAL
ejpam-3165	62	8	8(u	CARDINAL
ejpam-3165	62	9	8(u	ORDINAL
ejpam-3165	62	10	4	CARDINAL
ejpam-3165	62	11	4(u	MONEY
ejpam-3165	62	12	u)(u	ORG
ejpam-3165	62	13	+ 6(u	DATE
ejpam-3165	62	14	u)(v	NORP
ejpam-3165	62	15	4(u	CARDINAL
ejpam-3165	63	1	u)(v	NORP
ejpam-3165	63	2	4(u	CARDINAL
ejpam-3165	63	3	u)(v	NORP
ejpam-3165	63	4	8(u	CARDINAL
ejpam-3165	64	1	5	CARDINAL
ejpam-3165	64	2	4	CARDINAL
ejpam-3165	64	3	5	CARDINAL
ejpam-3165	64	4	v‖4 ≤ ‖u+ v‖4	FAC
ejpam-3165	64	5	1 4	CARDINAL
ejpam-3165	64	6	1 4	CARDINAL
ejpam-3165	64	7	‖v‖	ORG
ejpam-3165	64	8	0 ⇒	PERCENT
ejpam-3165	64	9	u)3 + 6(u	PRODUCT
ejpam-3165	64	10	+ 15(u	DATE
ejpam-3165	64	11	+ 20(u	DATE
ejpam-3165	64	12	u)(v	NORP
ejpam-3165	64	13	+ 15(u	DATE
ejpam-3165	64	14	u)(v	NORP
ejpam-3165	65	1	u)(v	PERSON
ejpam-3165	65	2	u)3 + 15(u	ORG
ejpam-3165	65	3	+ 15(u	DATE
ejpam-3165	65	4	u)(v	NORP
ejpam-3165	65	5	u)3 + 15(u	ORG
ejpam-3165	65	6	+ 15(u	DATE
ejpam-3165	65	7	u)(v	NORP
ejpam-3165	65	8	u)(v	PERSON
ejpam-3165	65	9	12(u	CARDINAL
ejpam-3165	66	1	u)(v	PERSON
ejpam-3165	66	2	u)(v	PERSON
ejpam-3165	68	1	6	CARDINAL
ejpam-3165	69	1	j. pure	PERSON
ejpam-3165	69	2	11	CARDINAL
ejpam-3165	69	3	1	CARDINAL
ejpam-3165	69	4	2018	DATE
ejpam-3165	69	5	352	CARDINAL
ejpam-3165	69	6	0 ⇒	PERCENT
ejpam-3165	69	7	6(u	CARDINAL
ejpam-3165	69	8	+ 15(u	DATE
ejpam-3165	69	9	u)(v	NORP
ejpam-3165	69	10	+ 15(u	DATE
ejpam-3165	69	11	u)(v	NORP
ejpam-3165	69	12	6(u	CARDINAL
ejpam-3165	69	13	u)(v	PERSON
ejpam-3165	69	14	u)3 + 15(u	ORG
ejpam-3165	69	15	+ 15(u	DATE
ejpam-3165	69	16	u)(v	NORP
ejpam-3165	70	1	u)(v	PERSON
ejpam-3165	70	2	u)3 + 15(u	ORG
ejpam-3165	70	3	+ 15(u	DATE
ejpam-3165	70	4	u)(v	NORP
ejpam-3165	70	5	12(u	CARDINAL
ejpam-3165	70	6	u)(v	PERSON
ejpam-3165	71	1	u)(v	PERSON
ejpam-3165	73	1	6	CARDINAL
ejpam-3165	73	2	1 6	CARDINAL
ejpam-3165	73	3	1 6	CARDINAL
ejpam-3165	73	4	‖v‖	ORG
ejpam-3165	75	1	nc4(u	GPE
ejpam-3165	75	2	v)2 +n	ORG
ejpam-3165	75	3	u) n−6 2	ORG
ejpam-3165	75	4	+ nc7(u	PERSON
ejpam-3165	75	5	2	CARDINAL
ejpam-3165	76	1	u, u	ORG
ejpam-3165	76	2	2	CARDINAL
ejpam-3165	76	3	0	CARDINAL
ejpam-3165	76	4	u	NORP
ejpam-3165	77	1	u) n−4 2	ORG
ejpam-3165	77	2	+ 1 5	DATE
ejpam-3165	78	1	u) n−6 2	ORG
ejpam-3165	79	1	2	CARDINAL
ejpam-3165	80	1	u	NORP
ejpam-3165	80	2	u) n−4 2	ORG
ejpam-3165	80	3	u) n−6 2	ORG
ejpam-3165	81	1	u	NORP
ejpam-3165	82	1	u) n−4 2	ORG
ejpam-3165	82	2	u) n−6 2	ORG
ejpam-3165	84	1	j. pure	PERSON
ejpam-3165	84	2	11	CARDINAL
ejpam-3165	84	3	1	CARDINAL
ejpam-3165	84	4	2018	DATE
ejpam-3165	84	5	352	CARDINAL
ejpam-3165	84	6	u	NORP
ejpam-3165	85	1	u) n−4 2	ORG
ejpam-3165	85	2	+ 1 5	DATE
ejpam-3165	86	1	u) n−6 2	ORG
ejpam-3165	87	1	2	CARDINAL
ejpam-3165	89	1	u	NORP
ejpam-3165	90	1	u) n−4 2	ORG
ejpam-3165	90	2	+ 1 5	DATE
ejpam-3165	91	1	u) n−6 2	ORG
ejpam-3165	92	1	2	CARDINAL
ejpam-3165	93	1	u	NORP
ejpam-3165	94	1	u) n−4 2	ORG
ejpam-3165	94	2	+ 1 5	DATE
ejpam-3165	95	1	u) n−6 2	ORG
ejpam-3165	96	1	2	CARDINAL
ejpam-3165	97	1	2	CARDINAL
ejpam-3165	98	1	u) n−4 2	ORG
ejpam-3165	98	2	+ 1 5	DATE
ejpam-3165	99	1	u) n−6 2	ORG
ejpam-3165	100	1	2	CARDINAL
ejpam-3165	101	1	2	CARDINAL
ejpam-3165	101	2	u) n−4 2	ORG
ejpam-3165	101	3	nc5(u	ORG
ejpam-3165	101	4	u) n−6 2	ORG
ejpam-3165	101	5	2	CARDINAL
ejpam-3165	102	1	u, u	ORG
ejpam-3165	102	2	2	CARDINAL
ejpam-3165	102	3	0	CARDINAL
ejpam-3165	102	4	u	NORP
ejpam-3165	103	1	u) n−4 2	ORG
ejpam-3165	103	2	+ 1 5	DATE
ejpam-3165	104	1	u) n−6 2	ORG
ejpam-3165	105	1	2	CARDINAL
ejpam-3165	106	1	u	NORP
ejpam-3165	106	2	u) n−4 2	ORG
ejpam-3165	106	3	u) n−6 2	ORG
ejpam-3165	107	1	u	NORP
ejpam-3165	108	1	u) n−4 2	ORG
ejpam-3165	108	2	+ 1 5	DATE
ejpam-3165	109	1	u) n−6 2	ORG
ejpam-3165	110	1	2	CARDINAL
ejpam-3165	111	1	u	NORP
ejpam-3165	111	2	u) n−4 2	ORG
ejpam-3165	111	3	u) n−6 2	ORG
ejpam-3165	113	1	j. pure	PERSON
ejpam-3165	113	2	11	CARDINAL
ejpam-3165	113	3	1	CARDINAL
ejpam-3165	113	4	2018	DATE
ejpam-3165	113	5	352	CARDINAL
ejpam-3165	113	6	358 ⇒ 2n(u	QUANTITY
ejpam-3165	113	7	u	NORP
ejpam-3165	114	1	u) n−4 2	ORG
ejpam-3165	114	2	+ 1 5	DATE
ejpam-3165	115	1	u) n−6 2	ORG
ejpam-3165	116	1	2	CARDINAL
ejpam-3165	117	1	u	NORP
ejpam-3165	118	1	u) n−4 2	ORG
ejpam-3165	118	2	+ 1 5	DATE
ejpam-3165	119	1	u) n−6 2	ORG
ejpam-3165	120	1	2	CARDINAL
ejpam-3165	121	1	2	CARDINAL
ejpam-3165	121	2	= ∥∥∥(u+ v)n ∥∥∥	PERSON
ejpam-3165	122	1	1)(n− 2)(u.u	DATE
ejpam-3165	122	2	+ 1 5	DATE
ejpam-3165	123	1	u) n−6 2	ORG
ejpam-3165	124	1	2	CARDINAL
ejpam-3165	125	1	9	CARDINAL
ejpam-3165	125	2	9	CARDINAL
ejpam-3165	125	3	v‖n ≤	FAC
ejpam-3165	126	1	1 n	QUANTITY
ejpam-3165	126	2	1	CARDINAL
ejpam-3165	127	1	‖v‖	ORG
ejpam-3165	127	2	10	CARDINAL
ejpam-3165	127	3	2.2	CARDINAL
ejpam-3165	128	1	10	CARDINAL
ejpam-3165	128	2	two	CARDINAL
ejpam-3165	129	1	2	CARDINAL
ejpam-3165	130	1	1	CARDINAL
ejpam-3165	130	2	two	CARDINAL
ejpam-3165	130	3	1	CARDINAL
ejpam-3165	130	4	1	CARDINAL
ejpam-3165	130	5	14	CARDINAL
ejpam-3165	131	1	barnes et al	PERSON
ejpam-3165	132	1	j. pure	PERSON
ejpam-3165	132	2	11	CARDINAL
ejpam-3165	132	3	1	CARDINAL
ejpam-3165	132	4	2018	DATE
ejpam-3165	132	5	352	CARDINAL
ejpam-3165	132	6	firstly	ORDINAL
ejpam-3165	132	7	two	CARDINAL
ejpam-3165	132	8	0	CARDINAL
ejpam-3165	132	9	u	NORP
ejpam-3165	132	10	+ 2(u	DATE
ejpam-3165	133	1	2(u	CARDINAL
ejpam-3165	133	2	v)‖	PRODUCT
ejpam-3165	133	3	11	CARDINAL
ejpam-3165	133	4	two	CARDINAL
ejpam-3165	133	5	v)| ≤	CARDINAL
ejpam-3165	133	6	2 + v2 2 ∣∣∣	QUANTITY
ejpam-3165	133	7	12	CARDINAL
ejpam-3165	133	8	2	CARDINAL
ejpam-3165	133	9	12	CARDINAL
ejpam-3165	133	10	11	CARDINAL
ejpam-3165	133	11	|u|2 + |v|2	PRODUCT
ejpam-3165	134	1	13	CARDINAL
ejpam-3165	134	2	two	CARDINAL
ejpam-3165	134	3	0	CARDINAL
ejpam-3165	135	1	u	NORP
ejpam-3165	135	2	+ 2(u	DATE
ejpam-3165	135	3	v)‖ = ‖(u+ v)2‖ ⇒ 2|(u	PERSON
ejpam-3165	135	4	|u|2 + |v|2	PRODUCT
ejpam-3165	135	5	14	CARDINAL
ejpam-3165	135	6	13	CARDINAL
ejpam-3165	135	7	14	CARDINAL
ejpam-3165	135	8	‖v‖	ORG
ejpam-3165	135	9	15	CARDINAL
ejpam-3165	135	10	360 3	DATE
ejpam-3165	136	1	1	CARDINAL
ejpam-3165	137	1	second	ORDINAL
ejpam-3165	137	2	2−	CARDINAL
ejpam-3165	137	3	two	CARDINAL
ejpam-3165	138	1	4	CARDINAL
ejpam-3165	139	1	1	CARDINAL
ejpam-3165	139	2	c. l. fleming	PERSON
ejpam-3165	139	3	s. e. griffis	PERSON
ejpam-3165	139	4	j. e. bell	PERSON
ejpam-3165	139	5	european journal of operational	ORG
ejpam-3165	139	6	224	CARDINAL
ejpam-3165	139	7	1	CARDINAL
ejpam-3165	140	1	1	CARDINAL
ejpam-3165	140	2	2	CARDINAL
ejpam-3165	140	3	b. kr	PERSON
ejpam-3165	140	4	patra	ORG
ejpam-3165	140	5	6	CARDINAL
ejpam-3165	141	1	469	CARDINAL
ejpam-3165	141	2	3	CARDINAL
ejpam-3165	141	3	a. m. fink	PERSON
ejpam-3165	141	4	249	CARDINAL
ejpam-3165	141	5	2000).pp	CARDINAL
ejpam-3165	141	6	118	CARDINAL
ejpam-3165	142	1	4	CARDINAL
ejpam-3165	142	2	h. p. mulholland	PERSON
ejpam-3165	142	3	minkowski	PERSON
ejpam-3165	142	4	london	GPE
ejpam-3165	143	1	2-51	CARDINAL
ejpam-3165	143	2	1	CARDINAL
ejpam-3165	143	3	1949	DATE
ejpam-3165	145	1	294-307	CARDINAL
ejpam-3165	146	1	5	CARDINAL
ejpam-3165	146	2	k-s. saito	PERSON
ejpam-3165	146	3	h. mizuguchi	PERSON
ejpam-3165	146	4	k-i. mitani	ORG
ejpam-3165	146	5	network(2011	ORG
ejpam-3165	148	1	5	CARDINAL
ejpam-3165	148	2	10.5402/2011/514184	CARDINAL
ejpam-3165	149	1	6	CARDINAL
ejpam-3165	149	2	k-i. mitani	ORG
ejpam-3165	149	3	k-s	PERSON
ejpam-3165	149	4	2010	DATE
ejpam-3165	151	1	17	CARDINAL
ejpam-3165	151	2	10.1155/2010/323609	CARDINAL
ejpam-3165	151	3	7	CARDINAL
ejpam-3165	151	4	s. saitoh	PERSON
ejpam-3165	152	1	4	CARDINAL
ejpam-3165	152	2	3	CARDINAL
ejpam-3165	152	3	2003	DATE
ejpam-3165	153	1	8	CARDINAL
ejpam-3165	153	2	k-i. mitani	PERSON
ejpam-3165	153	3	k-s	PERSON
ejpam-3165	153	4	central european journal of mathematics 12,	ORG
ejpam-3165	153	5	11	DATE
ejpam-3165	153	6	1615-1623	CARDINAL
ejpam-3165	153	7	9	CARDINAL
ejpam-3165	153	8	f. dadipour	PERSON
ejpam-3165	153	9	m.s. moslehian	PERSON
ejpam-3165	153	10	j. m. rassias	PERSON
ejpam-3165	153	11	s-e. takahasi	ORG
ejpam-3165	153	12	normed spaces	ORG
ejpam-3165	154	1	75	CARDINAL
ejpam-3165	154	2	2	CARDINAL
ejpam-3165	154	3	2012	DATE
ejpam-3165	156	1	735	CARDINAL
ejpam-3165	156	2	361	CARDINAL
ejpam-3165	156	3	10	CARDINAL
ejpam-3165	156	4	j. t. scheick	PERSON
ejpam-3165	156	5	prentice-hall, inc	ORG
ejpam-3165	156	6	new york	GPE
ejpam-3165	156	7	1997	DATE
ejpam-3165	157	1	11	CARDINAL
ejpam-3165	157	2	n. minculete	PERSON
ejpam-3165	157	3	r. pãltãnea	LOC
ejpam-3165	157	4	2017	CARDINAL
ejpam-3165	158	1	10.1186	CARDINAL
ejpam-3165	159	1	12	CARDINAL
ejpam-3165	159	2	j. t. oden	PERSON
ejpam-3165	159	3	first	ORDINAL
ejpam-3165	159	4	englewood cliffs	GPE
ejpam-3165	159	5	n.j	GPE
ejpam-3165	159	6	prentice-hall, 1979	ORG
ejpam-3165	160	1	13	CARDINAL
ejpam-3165	160	2	b. kolman	PERSON
ejpam-3165	160	3	d. r. hill	PERSON
ejpam-3165	160	4	prentice-hall, inc	ORG
ejpam-3165	160	5	new jersey	GPE
ejpam-3165	160	6	2000	DATE
ejpam-3165	161	1	14	CARDINAL
ejpam-3165	162	1	pearson education, inc	ORG
ejpam-3165	162	2	4th	ORDINAL
ejpam-3165	162	3	2010	DATE