Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 417089, 15 pages
doi:10.1155/2008/417089
A new hybrid iterative algorithm for fixed-point problems, variational inequality problems, and mixed equilibrium problems
Yonghong Yao1
, Yeong-Cheng Liou2
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
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.