System of Variational Inclusions and Fixed Points of Pseudocontractive Mappings in Banach Spaces

Abstract

The purpose of this paper is to solve the general system of variational inclusions (GSVI) with hierarchical variational inequality (HVI) constraint, for an infinite family of continuous pseudocontractive mappings in Banach spaces. By utilizing the equivalence between the GSVI and the fixed point problem, we construct an implicit multiple-viscosity approximation method for solving the GSVI. Under very mild conditions, we prove the strong convergence of the proposed method to a solution of the GSVI with the HVI constraint, for infinitely many pseudocontractions.Keywords: implicit multiple viscosity approximation method; system of variational inclusions; pseudocontractive mapping; nonexpansive mapping MSC: 47H05; 47H10; 47J25