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Journal of Applied Mathematics
Volume 2014, Article ID 193749, 10 pages
http://dx.doi.org/10.1155/2014/193749
Research Article

New Mixed Equilibrium Problems and Iterative Algorithms for Fixed Point Problems in Banach Spaces

1School of Mathematics and Sciences, Shijiazhuang University of Economics, Shijiazhuang 050031, China
2Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China

Received 30 October 2013; Accepted 16 December 2013; Published 9 January 2014

Academic Editor: Li Wei

Copyright © 2014 Minjiang Chen et al. 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 a new mixed equilibrium problem with a relaxed monotone mapping in Banach spaces and prove the existence of solutions of the equilibrium problem. Then we introduce a new iterative algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of fixed points of a quasi- -nonexpansive mapping and prove some strong convergence theorems of the iteration. Our results extend and improve the corresponding ones given by Wang et al., Takahashi and Zembayashi, and some others.