CONVERGENCE AND STABILITY OF ITERATIVE ALGORITHM OF SYSTEM OF GENERALIZED IMPLICIT VARIATIONAL-LIKE INCLUSION PROBLEMS USING (θ,φ,γ)-RELAXED COCOERCIVITY

Abstract

In this paper, we give the notion of M(.,.)-η-proximal mapping for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space and prove its existence and Lipschitz continuity. As an application, we introduce and investigate a new system of variational-like inclusions in Banach spaces. By means of M(.,.)-η-proximal mapping method, we give the existence of solution for the system of variational inclusions. Further, propose an iterative algorithm for finding the approximate solution of this class of variational inclusions. Furthermore, we discuss the convergence and stability analysis of the iterative algorithm. The results presented in this paper may be further expolited to solve some more important classes of problems in this direction.