Copyright © 2010 Min Liu 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.
We prove a
strong convergence theorem by using a hybrid method for finding a
common element of the set of solutions for generalized mixed
equilibrium problems, the set of fixed points of a family of
quasi--asymptotically nonexpansive mappings in strictly convex
reflexive Banach space with the Kadec-Klee property and, a
Fréchet differentiable norm under weaker conditions. The
method of the proof is different from, S. Takahashi and W. Takahashi that by (2008)
and that by Takahashi and Zembayashi (2008) and see references. It also shows that the
type of projection used in the iterative method is independent of
the properties of the mappings. The results presented in the paper
improve and extend some recent results.