H(., .)-φ-η-mixed accretive mapping with an application

Abstract

The motive of this article to introduce the notion called H(., .)-φ-η-mixed accretive mappings in Banach spaces. We generalized the idea of proximal-point mappings related with generalized m-accretive mappings to the H(., .)-φ-η-mixed accretive mappings and perusal its aspects single-valued property as well as Lipschitz continuity. Since proximal point mapping plays an important role to solve variational inclusion problems. Therefore, we design an iterative algorithm involving introduced proximal point mapping to solve variational inclusion problem. In last, we discuss its convergence with considerable assumptions.