Abstract
Let X be either uniformly smooth or a reflexive Banach space which has a weakly continuous duality map J(phi), with gauge phi. In this paper we propose an implicit iterative method and another explicit iterative method for solving a general system of valriational inequalities in X. These two methods are based on Korpelevich's extragradient method and Halpern's iterative method. Furthermore, we prove that under appropriate conditions the suggested algorithms converge strongly to some solutions of the considered general system of variational inequalities.