Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 362191, 21 pages
doi:10.1155/2009/362191
Strong convergence of an iterative method for equilibrium problems and variational inequality problems
Hongyu Li1
and Hongzhi Li2
1Department of Mathematics, TianJin Polytechnic University, TianJin 300160, China
2Department of Mathematics, Agricultural University of Hebei, BaoDing 071001, China
Abstract
We introduce an iterative method for finding a common element of the set of solutions of equilibrium problems, the set of solutions of variational inequality problems, and the set of fixed points of finite many nonexpansive mappings. We prove strong convergence of the iterative sequence generated by the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for the minimization problem.