SYSTEMS OF VARIATIONAL INEQUALITIES WITH HIERARCHICAL VARIATIONAL INEQUALITY CONSTRAINTS FOR LIPSCHITZIAN PSEUDOCONTRACTIONS

In this paper, we consider the problem of solving a general system of variational inequalities (GSVI) with a hierarchical variational inequality (HVI) constraint for countably many uniformly Lipschitzian pseudocontractive mappings and an accretive operator in a real Banach space. We propose an implicit composite extragradient-like method based on the Mann iteration method, the viscosity approximation method and the Korpelevich extragradient method. Convergence results for the proposed iteration method are also established under some suitable assumptions.