Copyright © 2010 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 iterative scheme for
finding the common element of the set of solutions of the generalized equilibrium
problems, the set of fixed points of an infinite
family of nonexpansive mappings, and the set of solutions of the
variational inequality problems for a relaxed -cocoercive and -Lipschitz continuous mapping in a real Hilbert space. Then, we
prove the strong convergence of a common element of the above three
sets under some suitable conditions. Our result can be considered as
an improvement and refinement of the previously known results.