Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand
Copyright © 2010 Siwaporn Saewan and Poom Kumam. 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 hybrid iterative scheme for finding a common element of the set
of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set
of the variational inequality for an -inverse-strongly monotone operator, the set of solutions of the
generalized mixed equilibrium problem and zeros of a maximal monotone operator in the framework of a
real Banach space. We obtain a strong convergence theorem for the sequences generated by this process
in a 2 uniformly convex and uniformly smooth Banach space. The results presented in this paper improve
and extend some recent results.