Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 417089, 15 pages
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

Academic Editor: Tomonari Suzuki

Copyright © 2008 Yonghong Yao et al. 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.


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.