Hybrid extragradient methods for asymptotically strict pseudo-contractions in the intermediate sense and variational inequality problems

Abstract

This article is devoted to investigating a new hybrid extragradient method for an asymptotically strict pseudo-contraction in the intermediate sense S and a monotone and Lipschitz continuous mapping A in a Hilbert space. The main purpose is to use this iterative method to generate a sequence for approximating a common element of the fixed point set of S and the solution set of the variational inequality problem for A. Weak convergence and strong convergence for the related sequences are established with respective iteration processes.