Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 564361, 15 pages
doi:10.1155/2010/564361
Research Article

An Iterative Algorithm for Mixed Equilibrium Problems and Variational Inclusions Approach to Variational Inequalities

Yeong-Cheng Liou

Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan

Received 13 September 2009; Revised 10 November 2009; Accepted 10 January 2010

Academic Editor: Nanjing Huang

Copyright © 2010 Yeong-Cheng Liou. 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 present an iterative algorithm for finding a common element x∗ of the set of solutions of a mixed equilibrium problem and the set of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithms strongly converge to x∗ which solves some variational inequality.