Copyright © 2013 Xueyong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An extension of subgradient method for solving variational inequality problems is presented. A new iterative process, which relates to the fixed point of a nonexpansive mapping and the current iterative point, is generated. A weak convergence theorem is obtained for three sequences generated by the iterative process under some mild conditions.