Set-Valued Variational Inclusion Governed by Generalized αiβj-Hp(., ., ...)-Accretive Mapping

Abstract

This work is concerned with the new notion called generalized αiβj-Hp(., ., ...)-accretive mapping that is the sum of two symmetric accretive mappings. It is an extension of the generalized αβ-H(., .)-accretive mapping. The proximal point mapping linked to the generalized αiβj-Hp(., ., ...)-accretive mappings is defined, and some of its characteristics are discussed. As an application of the new proximal point mapping, we consider a set-valued variational inclusion problem in q-uniformly smooth Banach spaces. Further, we propose an iterative scheme connected with αiβj-Hp(., ., ...)-proximal point mapping to find the solution of a variational inclusion problem and discuss its convergence criteria under appropriate assumptions. Some examples are constructed in support of generalized αiβj-Hp(., ., ...)-accretive mappings.