Hybrid viscosity implicit scheme for variational inequalities over the fixed point set of an asymptotically nonexpansive mapping in the intermediate sense in Banach spaces

Abstract

With the help of the generalized viscosity implicit method and hybrid steepest-descent method, we introduce an iterative scheme for approximating the solution of a variational inequality over the set of fixed points of an asymptotically nonexpansive mapping in the intermediate sense. Some strong convergence results for our proposed iterative scheme are established in the framework of Banach spaces. Applicability of our proposed method is shown in variational inclusion problem and convex minimization problem. We discuss some examples to demonstrate the numerical implementation and efficiency of our main results in comparison of other related results. Our results improve, extend and unify previously known results given in literature.