Graph Convergence and Iterative Approximation of Solution of a Set-Valued Variational Inclusions

Abstract

In this article, first, we introduce a class of proximal-point mapping associated with generalized ${\alpha }_i{\beta }_j$ - $H^p\left(.,.,\dots \right)$ -accretive mapping. Further, we discuss the graph convergence of generalized ${\alpha }_i{\beta }_j$ - $H^p\left(.,.,\dots \right)$ -accretive mapping. As an application, we consider a set-valued variational inclusion problem (SVIP) in real Banach spaces. Furthermore, we propose an iterative scheme involving the above class of proximal-point mapping to find a solution of SVIP and discuss its convergence under some convenient assumptions. An example is constructed and demonstrated few graphics in support of our main results.