THE STRUCTURE OF PROJECTION METHODS FOR VARIATIONAL INEQUALITY PROBLEMS AND WEAK CONVERGENCE THEOREMS

Abstract

In this paper, we study the structure of projection methods for variational inequality problems and then prove weak convergence theorems which generalize Takahashi and Toyoda [W. Takahashi and M. Toyoda, Weak convergence theorems for nonepxansive mappings and monotone mappings, J. Optim. Theory Appl. 118 (2003), 417–428] and Nadezhkina and Takahashi [N. Nadezhkina and W. Takahashi, Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl. 128 (2006), 191-201]. Our proofs are different from them. Furthermore, using these weak convergence theorems, we obtain some new results.