Abstract and Applied Analysis
Volume 2013 (2013), Article ID 107296, 13 pages
http://dx.doi.org/10.1155/2013/107296
Research Article

A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi- -Nonexpansive Mappings

Pongrus Phuangphoo1,2 and Poom Kumam1

1Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Kru, Bangkok 10140, Thailand
2Department of Mathematics, Faculty of Education, Bansomdejchaopraya Rajabhat University (BSRU), Thonburi, Bangkok 10600, Thailand

Received 28 July 2012; Revised 24 September 2012; Accepted 28 September 2012

Academic Editor: Yongfu Su

Copyright © 2013 Pongrus Phuangphoo and Poom Kumam. 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 modified Mann’s iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi- -nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions. Our result presented in this paper improves and generalizes some well-known results in the literature.