A General Composite Algorithms for Solving General Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

Rabian Wangkeeree, Thanatporn Bantaojai

Abstract

In this paper, we introduce a general composite algorithm for finding a common element of the set of solutions of an general equilibrium problem and the fixed point set a nonexpansive mapping in the framework of Hilbert spaces. Strong convergence of such iterative scheme is obtained which solving some variational inequalities for a strongly monotone and strictly pseudo-contractive mapping. Our results extend the corresponding recent results of Yao and Liou [Y. Yao, Y.C. Liou, Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems, Abstract and Applied Analysis, Volume 2010 (2010), Article ID 763506, 19 pages].