Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 531308, 20 pages
doi:10.1155/2009/531308
An iterative method for generalized equilibrium problems, fixed point problems and variational inequality problems
Qing-You Liu1
, Wei-You Zeng2
and Nan-Jing Huang2
1State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, China
2Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
Abstract
We introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of generalized equilibrium problems, the set of common fixed points of infinitely many nonexpansive mappings, and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in Hilbert spaces. We give some strong-convergence theorems under mild assumptions on parameters. The results presented in this paper improve and generalize the main result of Yao et al. (2007).