Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 372975, 18 pages
doi:10.1155/2011/372975
Research Article

New Iterative Scheme for Finite Families of Equilibrium, Variational Inequality, and Fixed Point Problems in Banach Spaces

Shenghua Wang1,2 and Caili Zhou3

1School of Applied Mathematics and Physics, North China Electric Power University, Baoding 071003, China
2Department of Mathematics, Gyeongsang National University, Jinju 660-714, Republic of Korea
3College of Mathematics and Computer, Hebei University, Baoding 071002, China

Received 6 December 2010; Accepted 30 January 2011

Academic Editor: S. Al-Homidan

Copyright © 2011 Shenghua Wang and Caili Zhou. 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 introduced a new iterative scheme for finding a common element in the set of common fixed points of a finite family of quasi-ϕ-nonexpansive mappings, the set of common solutions of a finite family of equilibrium problems, and the set of common solutions of a finite family of variational inequality problems in Banach spaces. The proof method for the main result is simplified under some new assumptions on the bifunctions.