A Modified Subgradient Extragradeint Method for Variational Inequality Problems and Fixed Point Problems in Real Banach Spaces

Abstract

Let E be a 2-uniformly convex and uniformly smooth real Banach space with dual space E ∗ . Let A : C → E ∗ be a monotone and Lipschitz continuous mapping and U : C → C be relatively non- expansive. An algorithm for approximating the common elements of the set of fixed points of a relatively nonexpansive map U and the set of solutions of a variational inequality problem for the monotone and Lipschitz continuous map A in E is constructed and proved to converge strongly.