Copyright © 2010 Peichao Duan and Jing Zhao. 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.

Abstract

Let {Si}i=1N be N strict pseudocontractions defined on a closed convex subset C of a real Hilbert space H. Consider the problem of finding a common element of the set of fixed point of these mappings and the set of solutions of an equilibrium problem with the parallel and cyclic algorithms. In this paper, we propose new iterative schemes for solving this problem and prove these schemes converge strongly by hybrid methods.