Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok 10140, Thailand
Copyright © 2009 Chaichana Jaiboon 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 extragradient viscosity approximation method
for finding the common element of the set of equilibrium problems, the set of solutions of fixed points of
an infinitely many nonexpansive mappings, and the set of solutions of the variational inequality problems
for -inverse-strongly monotone mapping in Hilbert spaces. Then, we prove the strong convergence of
the proposed iterative scheme to the unique solution of variational inequality, which is the optimality
condition for a minimization problem. Results obtained in this paper improve the previously known
results in this area.