Copyright © 2012 Shuo Sun. 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.

Abstract

We introduce a new regularization iterative algorithm for equilibrium and fixed point problems of nonexpansive mapping. Then, we prove a strong convergence theorem for nonexpansive mappings to solve a unique solution of the variational inequality and the unique sunny nonexpansive retraction. Our results extend beyond the results of S. Takahashi and W. Takahashi (2007), and many others.