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.
"An Alternative Regularization Method for Equilibrium Problems and Fixed Point of Nonexpansive Mappings." J. Appl. Math. 2012 (SI03) 1 - 16, 2012. https://doi.org/10.1155/2012/202860