Approximation of a Solution Associated to General Class of Variational Inclusions Involving Generalized αiβj-(Hp,φ)-η-Accretive Mappings

Abstract

This manuscript aims to define and study of a class of generalized αiβj-(Hp,φ)-η-accretive mappings and its associated class of proximal-point mappings. This generalized αiβj-(Hp,φ)-η-accretive mapping is the sum of two symmetric accretive mappings and an extension of the generalized αβ-H(., .)-accretive mapping. Further, we discuss the graph convergence of generalized αiβj-(Hp,φ)-η-accretive mappings. As an application, we consider a set-valued variational-like inclusion problem (SVLIP, in short) in semi-inner product spaces. Furthermore, we propose an iterative scheme and discuss the convergence analysis of the sequences generated from the proposed iterative algorithm. Some examples are constructed and demonstrate a few graphics for the convergence of proximal-point mapping.