Hybrid viscosity approximation methods for general systems of variational inequalities in Banach spaces

Let X be a uniformly convex and 2-uniformly smooth Banach space.In this paper, we propose an implicit iterative method and an explicit iterative method for solving a general system of variational inequalities (in short, GSVI) in X based on Korpelevich's extragradient method and viscosity approximation method.We show that the proposed algorithms converge strongly to some solutions of the GSVI under consideration.When X is a 2-uniformly smooth Banach space with weakly sequentially continuous duality mapping, we also propose two methods, which were inspired and motivated by Korpelevich's extragradient method and Mann's iterative method.Furthermore, it is also proven that the proposed algorithms converge strongly to some solutions of the considered GSVI.