Journal of Applied Mathematics
Volume 2012 (2012), Article ID 712651, 21 pages
http://dx.doi.org/10.1155/2012/712651
Research Article

A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators

Yaqin Wang1,2

1Mathematical College, Sichuan University, Chengdu, Sichuan 610064, China
2Department of Mathematics, Shaoxing University, Shaoxing 312000, China

Received 5 August 2011; Accepted 10 October 2011

Academic Editor: Ya Ping Fang

Copyright © 2012 Yaqin Wang. 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 introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality, the set of solutions of the generalized mixed equilibrium problem, and zeros of maximal monotone operators in a Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. The results obtained in this paper improve and extend the result of Zeng et al. (2010) and many others.