Variational Inclusion Governed by αβ-H((., .), (., .))-Mixed Accretive Mapping

Abstract

In this paper, we look into a new concept of accretive mappings called αβ-H((.,.),(.,.))mixed accretive mappings in Banach spaces. We extend the concept of proximal-point mappings
connected with generalized $m$-accretive mappings to the
 αβ-H((.,.),(.,.))-mixed accretive mappings and discuss its characteristics like single-valuable and Lipschitz continuity. Some illustration are given in support of  αβ-H((.,.),(.,.))-mixed accretive
mappings. Since proximal point mapping is a powerful tool for solving variational inclusion. Therefore, As an application of introduced mapping, we construct an iterative algorithm to solve variational inclusions and show its convergence with acceptable assumptions.