Strong Convergence of Common Solution of Variational Inequality and Fixed Point of an Asymptotically Pseudocontractive Mapping

Abstract

Variational inequality provides techniques for solving a variety of applied problems in Science and Engineering. The fixed point formulation of any variational inequality problem is not only useful for existence of solution of the variational inequality problem, but it also provides the facility to develop algorithms for approximation of solution of variational inequality problem.In this paper, we propose an iterative algorithm for solving a variational inequality problem over the set of common fixed point of asymptotically pseudocontractive mapping in a real Hilbert space. We have proved some strong convergence results. Our result improves and extends many corresponding results in the recent literature.