id	sid	eid	entity	type
ejpam-259	1	1	5_tallafha.dvi	CARDINAL
ejpam-259	1	2	european journal	ORG
ejpam-259	2	1	2	CARDINAL
ejpam-259	2	2	2, 2009	DATE
ejpam-259	2	3	231-238	CARDINAL
ejpam-259	2	4	1307-5543	CARDINAL
ejpam-259	2	5	a. tallafha∗	PERSON
ejpam-259	2	6	r. khalil university	PERSON
ejpam-259	2	7	jordan	GPE
ejpam-259	2	8	amman	GPE
ejpam-259	8	1	41a65	CARDINAL
ejpam-259	8	2	41a99	CARDINAL
ejpam-259	9	1	1	CARDINAL
ejpam-259	9	2	dx	ORG
ejpam-259	9	3	x×x	ORG
ejpam-259	9	4	dx	ORG
ejpam-259	10	1	∈	ORG
ejpam-259	10	2	∈	ORG
ejpam-259	10	3	dx	ORG
ejpam-259	11	1	dx	ORG
ejpam-259	12	1	r. khalil	PERSON
ejpam-259	13	1	231	CARDINAL
ejpam-259	13	2	2009	DATE
ejpam-259	14	1	a. tallafha	PERSON
ejpam-259	14	2	r. khalil	PERSON
ejpam-259	15	1	j. pure	PERSON
ejpam-259	15	2	2	CARDINAL
ejpam-259	15	3	2009	DATE
ejpam-259	15	4	231-238	CARDINAL
ejpam-259	15	5	232	CARDINAL
ejpam-259	15	6	γ	GPE
ejpam-259	15	7	∩ v2 ∈	PERSON
ejpam-259	15	8	u ◦ u ⊂	ORG
ejpam-259	15	9	∈	ORG
ejpam-259	15	10	∈	ORG
ejpam-259	15	11	w ∈	ORG
ejpam-259	16	1	1	CARDINAL
ejpam-259	16	2	2	CARDINAL
ejpam-259	18	1	normed	ORG
ejpam-259	18	2	3	CARDINAL
ejpam-259	18	3	4	CARDINAL
ejpam-259	19	1	normed	ORG
ejpam-259	20	1	2	CARDINAL
ejpam-259	21	1	≤ v2 means v1 ⊆ v2	PRODUCT
ejpam-259	22	1	1.1	CARDINAL
ejpam-259	23	1	⋃	DATE
ejpam-259	25	1	2.1	CARDINAL
ejpam-259	27	1	y −	PERSON
ejpam-259	29	1	0	CARDINAL
ejpam-259	31	1	dx	ORG
ejpam-259	31	2	dx	ORG
ejpam-259	31	3	⋃	DATE
ejpam-259	31	4	∈	ORG
ejpam-259	31	5	∈	ORG
ejpam-259	33	1	tallafha	GPE
ejpam-259	33	2	r. khalil	PERSON
ejpam-259	34	1	j. pure	PERSON
ejpam-259	34	2	2	CARDINAL
ejpam-259	34	3	2009	DATE
ejpam-259	34	4	231-238	CARDINAL
ejpam-259	34	5	233	CARDINAL
ejpam-259	35	1	normed	ORG
ejpam-259	40	1	∈	ORG
ejpam-259	44	1	3.1	CARDINAL
ejpam-259	46	1	ρ(x	PERSON
ejpam-259	49	1	4.1	CARDINAL
ejpam-259	51	1	ρ(x	PERSON
ejpam-259	52	1	ρ(x	PERSON
ejpam-259	54	1	ρ(x	PERSON
ejpam-259	54	2	y)⊆ ρ(x	PERSON
ejpam-259	55	1	d(x	ORG
ejpam-259	57	1	2	CARDINAL
ejpam-259	58	1	ρ(x	PERSON
ejpam-259	59	1	ρ(x	PERSON
ejpam-259	59	2	∈	ORG
ejpam-259	62	1	5.1	CARDINAL
ejpam-259	63	1	ρ(x	PERSON
ejpam-259	63	2	y ∈ e ρ(x	PERSON
ejpam-259	64	1	ρ(x	PERSON
ejpam-259	64	2	6.1	CARDINAL
ejpam-259	65	1	∈	ORG
ejpam-259	66	1	ρ(x	PERSON
ejpam-259	66	2	⊆	CARDINAL
ejpam-259	66	3	b(y	GPE
ejpam-259	66	4	⊆	CARDINAL
ejpam-259	67	1	a. tallafha	PERSON
ejpam-259	67	2	r. khalil	PERSON
ejpam-259	68	1	j. pure	PERSON
ejpam-259	68	2	2	CARDINAL
ejpam-259	68	3	2009	DATE
ejpam-259	68	4	231-238	CARDINAL
ejpam-259	68	5	234	CARDINAL
ejpam-259	68	6	7.1	CARDINAL
ejpam-259	69	1	⊆	CARDINAL
ejpam-259	69	2	⊆	CARDINAL
ejpam-259	69	3	∈	ORG
ejpam-259	69	4	∈	ORG
ejpam-259	70	1	8.1	CARDINAL
ejpam-259	72	1	∈	ORG
ejpam-259	73	1	j ρ(x	PERSON
ejpam-259	74	1	9.1	CARDINAL
ejpam-259	76	1	j ρ(x	PERSON
ejpam-259	79	1	ρ(x	PERSON
ejpam-259	80	1	ρ(x	PERSON
ejpam-259	82	1	∈	ORG
ejpam-259	82	2	ρ(x	PERSON
ejpam-259	82	3	⊆	CARDINAL
ejpam-259	84	1	10.1	CARDINAL
ejpam-259	85	1	∈	ORG
ejpam-259	85	2	xn	ORG
ejpam-259	85	3	xm	ORG
ejpam-259	85	4	≥ k.	PERSON
ejpam-259	86	1	11.1	CARDINAL
ejpam-259	88	1	j ρ(x	PERSON
ejpam-259	90	1	12.1	CARDINAL
ejpam-259	96	1	∈	ORG
ejpam-259	96	2	u ◦ u ⊂	ORG
ejpam-259	98	1	xm	ORG
ejpam-259	99	1	xm	ORG
ejpam-259	100	1	xn	ORG
ejpam-259	100	2	xm	ORG
ejpam-259	100	3	∈	ORG
ejpam-259	101	1	∈	ORG
ejpam-259	101	2	xn	ORG
ejpam-259	101	3	xm	ORG
ejpam-259	101	4	≥ k. let u	PERSON
ejpam-259	101	5	xk−1	ORG
ejpam-259	101	6	⊆	CARDINAL
ejpam-259	102	1	a. tallafha	PERSON
ejpam-259	102	2	r. khalil	PERSON
ejpam-259	103	1	j. pure	PERSON
ejpam-259	103	2	2	CARDINAL
ejpam-259	103	3	2009	DATE
ejpam-259	103	4	231-238	CARDINAL
ejpam-259	103	5	235	CARDINAL
ejpam-259	104	1	⊆	CARDINAL
ejpam-259	104	2	w	GPE
ejpam-259	104	3	∪v	ORG
ejpam-259	104	4	13.1	CARDINAL
ejpam-259	109	1	w	GPE
ejpam-259	109	2	w	GPE
ejpam-259	109	3	w. hence	GPE
ejpam-259	111	1	∈ γ	ORG
ejpam-259	112	1	⊆	CARDINAL
ejpam-259	113	1	xn→	ORG
ejpam-259	118	1	14.1	CARDINAL
ejpam-259	119	1	3	CARDINAL
ejpam-259	120	1	ρ(x	PERSON
ejpam-259	120	2	15.1	CARDINAL
ejpam-259	121	1	ρ(x	PERSON
ejpam-259	124	1	∞ ∩ n	PERSON
ejpam-259	125	1	ρ(x	PERSON
ejpam-259	126	1	y ∈ e ρ(x	PERSON
ejpam-259	127	1	ρ(x	PERSON
ejpam-259	128	1	16.1	CARDINAL
ejpam-259	131	1	two	CARDINAL
ejpam-259	132	1	6=	CARDINAL
ejpam-259	132	2	6=	CARDINAL
ejpam-259	133	1	γ	GPE
ejpam-259	134	1	w ∈	PERSON
ejpam-259	134	2	w	GPE
ejpam-259	134	3	w	GPE
ejpam-259	134	4	∩ b(y	LOC
ejpam-259	134	5	6=	CARDINAL
ejpam-259	136	1	w.	PERSON
ejpam-259	136	2	w	GPE
ejpam-259	136	3	∈	ORG
ejpam-259	138	1	a. tallafha	PERSON
ejpam-259	138	2	r. khalil	PERSON
ejpam-259	139	1	j. pure	PERSON
ejpam-259	139	2	2	CARDINAL
ejpam-259	139	3	2009	DATE
ejpam-259	139	4	231-238	CARDINAL
ejpam-259	139	5	236	CARDINAL
ejpam-259	139	6	∩ b(y	LOC
ejpam-259	140	1	φ	PERSON
ejpam-259	141	1	e. clearly	PERSON
ejpam-259	142	1	3	CARDINAL
ejpam-259	144	1	1.2	CARDINAL
ejpam-259	146	1	ρ(x	PERSON
ejpam-259	147	1	ρ(x	PERSON
ejpam-259	148	1	2.2	CARDINAL
ejpam-259	151	1	11.1	CARDINAL
ejpam-259	151	2	ρ(x	PERSON
ejpam-259	151	3	ρ(x	PERSON
ejpam-259	152	1	ρ(x	PERSON
ejpam-259	154	1	normed	ORG
ejpam-259	154	2	4	CARDINAL
ejpam-259	156	1	4	CARDINAL
ejpam-259	159	1	2.3	CARDINAL
ejpam-259	164	1	ρ(x	PERSON
ejpam-259	164	2	1 ρ(x	PERSON
ejpam-259	165	1	two	CARDINAL
ejpam-259	165	2	ρ(x	PERSON
ejpam-259	165	3	ρ(x	PERSON
ejpam-259	165	4	one	CARDINAL
ejpam-259	166	1	ρ(x	PERSON
ejpam-259	167	1	ρ(x	PERSON
ejpam-259	167	2	a. tallafha	PERSON
ejpam-259	167	3	r. khalil	PERSON
ejpam-259	168	1	j. pure	PERSON
ejpam-259	168	2	2	CARDINAL
ejpam-259	168	3	2009	DATE
ejpam-259	168	4	231-238	CARDINAL
ejpam-259	168	5	237	CARDINAL
ejpam-259	169	1	1 ρ(x	PERSON
ejpam-259	169	2	ρ(x	PERSON
ejpam-259	169	3	1 ≤ k ≤ n. hence e	QUANTITY
ejpam-259	170	1	2.4	CARDINAL
ejpam-259	171	1	1	CARDINAL
ejpam-259	173	1	∈	ORG
ejpam-259	174	1	ρ(x	PERSON
ejpam-259	174	2	1 ei	CARDINAL
ejpam-259	174	3	y ∈	PERSON
ejpam-259	175	1	i=1 ei ρ(x	PERSON
ejpam-259	176	1	1	CARDINAL
ejpam-259	176	2	y ∈ei ρ(x	PERSON
ejpam-259	177	1	y ∈ei ρ(x	PERSON
ejpam-259	178	1	ρ(x	PERSON
ejpam-259	179	1	ρ(x	PERSON
ejpam-259	179	2	1 ei	CARDINAL
ejpam-259	181	1	1 ρ(x	PERSON
ejpam-259	181	2	ρ(x	PERSON
ejpam-259	181	3	1	CARDINAL
ejpam-259	181	4	2	DATE
ejpam-259	182	1	ρ(x	PERSON
ejpam-259	182	2	1 ei	CARDINAL
ejpam-259	184	1	1 ρ(x	PERSON
ejpam-259	184	2	ρ(x	PERSON
ejpam-259	184	3	∈	ORG
ejpam-259	184	4	1 ei	CARDINAL
ejpam-259	186	1	2.5	CARDINAL
ejpam-259	188	1	1	CARDINAL
ejpam-259	188	2	2	CARDINAL
ejpam-259	189	1	y = lim yn	PERSON
ejpam-259	191	1	ρ(x	PERSON
ejpam-259	192	1	ρ(x	PERSON
ejpam-259	193	1	ρ(x	PERSON
ejpam-259	193	2	6=∆	CARDINAL
ejpam-259	193	3	ρ(x	PERSON
ejpam-259	194	1	⊆	CARDINAL
ejpam-259	194	2	ρ(x	PERSON
ejpam-259	195	1	ρ(x	PERSON
ejpam-259	195	2	ρ(x	PERSON
ejpam-259	195	3	2.3	CARDINAL
ejpam-259	197	1	mn	ORG
ejpam-259	197	2	ρ(x	PERSON
ejpam-259	197	3	ρ(x	PERSON
ejpam-259	197	4	∩ ρ(x	PERSON
ejpam-259	197	5	ymn−1	ORG
ejpam-259	200	1	yn).now	DATE
ejpam-259	200	2	ρ(x	PERSON
ejpam-259	201	1	⊆	CARDINAL
ejpam-259	202	1	∈	ORG
ejpam-259	202	2	wj ∈ γ	PERSON
ejpam-259	202	3	2wj	CARDINAL
ejpam-259	202	4	2wj	CARDINAL
ejpam-259	202	5	⊆	CARDINAL
ejpam-259	202	6	wj	PERSON
ejpam-259	202	7	wj+1.if ∞	PERSON
ejpam-259	202	8	wj �	PERSON
ejpam-259	203	1	a. tallafha	PERSON
ejpam-259	203	2	r. khalil	PERSON
ejpam-259	204	1	j. pure	PERSON
ejpam-259	204	2	2	CARDINAL
ejpam-259	204	3	2009	DATE
ejpam-259	204	4	231-238	CARDINAL
ejpam-259	204	5	238	CARDINAL
ejpam-259	204	6	⊆	CARDINAL
ejpam-259	204	7	2wj	CARDINAL
ejpam-259	204	8	2wj	CARDINAL
ejpam-259	204	9	⊆	CARDINAL
ejpam-259	205	1	w	ORG
ejpam-259	205	2	⊆	CARDINAL
ejpam-259	206	1	1	CARDINAL
ejpam-259	206	2	r.	NORP
ejpam-259	206	3	north-holand	GPE
ejpam-259	206	4	amsterdam	GPE
ejpam-259	206	5	1968	DATE
ejpam-259	207	1	2	CARDINAL
ejpam-259	207	2	i.m.	PERSON
ejpam-259	207	3	topological	ORG
ejpam-259	209	1	springer-verlag 1987	ORG
ejpam-259	210	1	3	CARDINAL
ejpam-259	210	2	w.	PERSON
ejpam-259	210	3	cheney	PERSON
ejpam-259	210	4	e. approximation	PERSON
ejpam-259	212	1	1169	CARDINAL
ejpam-259	213	1	springer verlag	PERSON
ejpam-259	213	2	new york	GPE
ejpam-259	213	3	1985	DATE
ejpam-259	214	1	4	CARDINAL
ejpam-259	214	2	i. best approximation	ORG
ejpam-259	214	3	normed linear spaces	ORG
ejpam-259	214	4	new york	GPE
ejpam-259	214	5	1970	DATE