Copyright © 2009 Yonghong Yao et al. 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.
The purpose of this paper is to investigate the problem of approximating a common element of the set of fixed points of a demicontractive mapping and the set of solutions of a mixed equilibrium problem. First, we
propose an extragradient method for solving the mixed equilibrium problems
and the fixed point problems. Subsequently, we prove the strong convergence of the proposed algorithm under some mild assumptions.