Fixed Point Theory and Applications 
Volume 2008 (2008), Article ID 417089, 15 pages
doi:10.1155/2008/417089
Research Article

A New Hybrid Iterative Algorithm for Fixed-Point Problems, Variational Inequality Problems, and Mixed Equilibrium Problems

Yonghong Yao,1 Yeong-Cheng Liou,2 and Jen-Chih Yao3

 1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
3Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan
Received 29 August 2007; Accepted 6 February 2008

Recommended by Tomonari Suzuki

Abstract

We introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of the variational inequality of a monotone mapping, and the set of solutions of a mixed equilibrium problem. This study, proves a strong convergence theorem by the proposed hybrid iterative algorithm which solves fixed-point problems, variational inequality problems, and mixed equilibrium problems.