id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ijassa-305	Saewan, Siwaporn; Kumam, Poom	A New Modified Block Iterative Algorithm for a System of Equilibrium Problems and a Fixed Point Set of Uniformly Quasi-φ-Asymptotically Nonexpansive Mappings	2011	26	.pdf	application/pdf	11672	564	77	‖xn‖2 − (‖p‖2 − 2〈p, Jun〉+ ‖un‖2) + θn = ‖xn‖2 − ‖un‖2 − 2〈p, Jxn − Jun〉+ θn ≤ ‖xn − un‖(‖xn + un‖) + 2‖p‖‖Jxn − Jun‖+ θn. (60) From (36), (37), θn → 0 as n→∞ and Lemma 2.4, we get lim n→∞ ‖un − Ωj nyn‖ = 0∀j = 1, 2, 3, ...,m. (61) By using triangle inequality, we have ‖xn − Ωj nyn‖ ≤ ‖xn − un‖+ ‖un − Ωj nyn‖. From (36) and (61), we have lim n→∞ ‖xn − Ωj nyn‖ = 0 ∀j = 1, 2, 3, ...,m. (62) Again by using triangle inequality, we have ‖Ωj nyn − Ωj−1 n yn‖ ≤ ‖Ωj nyn − xn‖+ ‖xn − Ωj−1 n yn‖. From (62),we also have lim n→∞ ‖Ωj nyn − Ωj−1 n yn‖ = 0 ∀j = 1, 2, 3, ...,m. (63) such that, for any positive integer i, j with i < j, ‖ ∞∑ n=1 λnxn‖2 ≤ ∞∑ n=1 λn‖xn‖2 − λiλjg(‖xi − xj‖).	cache/ijassa-305.pdf	txt/ijassa-305.txt