Copyright © 2009 Jian-Wen Peng and Soon-Yi Wu. 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.
We introduce a new approximation scheme combining the viscosity method with extragradient method for finding a common element of the set of solutions of a mixed equilibrium problem and the set of fixed points of a finite family of
nonexpansive mappings and the set of the variational inequality for a monotone, Lipschitz continuous mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result, we also get some new and interesting results. The results in this paper generalize, extend, and improve some well-known results in