Mann-type algorithms for variational inequality problems and fixed point problems

Abstract

The purpose of this paper is to investigate the problem of finding a common element of the solution set of a variational inequality problem for a monotone, Lipschitz-continuous mapping and set of fixed point of a quasi-nonexpansive mapping. We introduce Mann-type Tseng's extragradient-like approximation method which is based on so-called inertial Tseng's extragradient method and Mann method. We establish two weak convergence theorems for two iterative sequences generated by these methods. Our results extend and improve some related results in the literatures.