Viscosity Approximation Methods for a General Variational Inequality System and Fixed Point Problems in Banach Spaces

Abstract

In Banach spaces, we study the problem of solving a more general variational inequality system for an asymptotically non-expansive mapping. We give a new viscosity approximation scheme to find a common element. Some strong convergence theorems of the proposed iterative method are obtained. A numerical experiment is given to show the implementation and efficiency of our main theorem. Our results presented in this paper generalize and complement many recent ones.

Keywords

• strong convergence
• fixed point
• general variational inequality system
• asymptotically non-expansive mapping
• banach space