On viscosity iterative methods for variational inequalities

Let be a commutative family of nonexpansive mappings of a closed convex subset C of a reflexive Banach space X such that the set of common fixed point is nonempty. In this paper, we suggest and analyze a new viscosity iterative method for a commutative family of nonexpansive mappings. We also prove that the approximate solution obtained by the proposed method converges to a solution of a variational inequality. Our method of proof is simple and different from the other methods. Results proved in this paper may be viewed as an improvement and refinement of the previously known results.