WEAK AND STRONG CONVERGENCE THEOREMS FOR VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS WITH TSENG’S EXTRAGRADIENT METHOD

Abstract

The paper is concerned with the problem of finding a common solution of a variational inequality problem governed by Lipschitz continuous monotone mappings and of a fixed point problem of nonexpansive mappings. To solve this problem, we introduce two new iterative algorithms which are based on Tseng's extragradient method. Moreover we prove the weak and strong convergence of these new algorithms to a solution of the above-stated problem.