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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 619762, 9 pages
http://dx.doi.org/10.1155/2013/619762
Research Article

Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces

1Department of Applied Mathematics and Physics, North China Electric Power University, Baoding 071003, China
2Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 1 February 2013; Accepted 9 March 2013

Academic Editor: Yisheng Song

Copyright © 2013 Shenghua Wang and Shin Min Kang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.