EXISTENCE AND APPROXIMATION OF SOLUTION OF THE VARIATIONAL INEQUALITY PROBLEM WITH A SKEW MONOTONE OPERATOR DEFINED ON THE DUAL SPACES OF BANACH SPACES

Abstract

In this paper, we first study an existence theorem of the variational inequality problem for a skew monotone operator defined on the dual space of a smooth Banach space. Secondary, we prove a weak convergence theorem for finding a solution of the variational inequality problem by using projection algorithm method with a new projection which was introduced by Ibaraki and Takahashi [T. Ibaraki, W. Takahashi, A new projection and convergence theorems for the projections in Banach spaces, Journal of Approximation Theory 149 (2007),1-14]. Further, we apply our convergence theorem to the convex minimization problem and the problem of finding a zero point of the maximal skew monotone operator