Copyright © 2011 Shenghua Wang and Baohua Guo. 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 an iterative algorithm for finding a common element of the
set of solutions of an infinite family of equilibrium problems and the set of fixed points of a finite
family of nonexpansive mappings in a Hilbert space. We prove some strong convergence theorems for
the proposed iterative scheme to a fixed point of the family of nonexpansive mappings, which is the
unique solution of a variational inequality. As an application, we use the result of this paper to solve
a multiobjective optimization problem. Our result extends and improves the ones of Colao et al. (2008) and some others.