H-Mixed Accretive Mapping and Proximal Point Method for Solving a System of Generalized Set-Valued Variational Inclusions

Abstract

In this paper, we introduce a new system of variational inclusion problems called system of generalized set-valued variational inclusion problems involving -mixed accretive mapping in q-uniformly smooth Banach spaces. By means of proximal-point mapping method, we prove the existence of solution of this system of variational inclusions. Further, we propose an iterative algorithm for finding the approximate solution of the system. Furthermore, we prove that the sequences generated by the iterative algorithm converge strongly to a solution of the system.