Convergence of Common Solution of Variational Inequality and Fixed Point of a Pseudocontractive Mapping

Abstract

Variational inequalities arise in models for a large number of mathematical, physical, economics, finance, optimization, game theory, engineering, and other problems. The fixed point formulation of any variational inequality problem is not only useful for the existence of solution of the variational inequality problem, but it also provides the facility to develop algorithms for the approximation of solution of variational inequality problem. A lot of research has been carried out to approximate common solution of fixed point of nonexpansive mapping and solution of a variational inequality. In this paper, we propose an iterative algorithm which gives a common element of fixed point of asymptotically pseudocontractive mapping and a certain variational inequality. Our result extends the previously known results from Hilbert Space to Banach Space and from asymptotically nonexpansive mapping to asymptotically pseudocontractive mapping.