A System of Multi-Valued Variational Inclusions Involving P-Accretive Mappings in Real Uniformly Smooth Banach Spaces

Faizan Ahmad Khan, Saleh A. Al-Mezel, Kaleem R. Kazmi

Abstract

In this paper, we consider a class of accretive mappings called P-accretive mappings in real Banach spaces. We prove that the proximal-point mapping of the  P-accretive mapping is single-valued and Lipschitz continuous. Further, we consider a system of multi-valued variational inclusions involving P-accretive mappings in real uniformly smooth Banach spaces. Using proximal-point mapping method, we prove the existence of solution and discuss the convergence analysis of iterative algorithm for the system of multi-valued variational inclusions. The theorems presented in this paper extend and improve many known results in the literature.