Abstract and Applied Analysis
Volume 2011 (2011), Article ID 562689, 24 pages
http://dx.doi.org/10.1155/2011/562689
Research Article

A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality Problem

Atid Kangtunyakarn

Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand

Received 7 October 2010; Revised 25 January 2011; Accepted 11 February 2011

Academic Editor: Norimichi Hirano

Copyright © 2011 Atid Kangtunyakarn. 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 iterative scheme and a new mapping generated by infinite family of nonexpansive mappings and infinite real number. By using both of these ideas, we obtain strong convergence theorem for finding a common element of the set of solution of equilibrium problem and the set of variational inequality and the set of fixed-point problems of infinite family of nonexpansive mappings. Moreover, we apply our main result to obtain strong convergence theorems for finding a common element of the set of solution of equilibrium problem and the set of variational inequality and the set of common fixed point of pseudocontractive mappings.