WEAK CONVERGENCE THEOREM BY A MODIFIED EXTRAGRADIENT METHOD FOR NONEXPANSIVE MAPPINGS AND MONOTONE MAPPINGS

In this paper, we introduce a modified extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone and Lipschitz continuous mapping. Our modified extragradient method is a variant of the so-called extragradient method. We obtain a weak convergent theorem for two sequences generated by this modified extragradient method.