Fixed points of Osilike-Berinde-G-nonexpansive mappings in metric spaces endowed with graphs

Abstract

In this paper, we introduce the notion of Osilike-Berinde-G-nonexpansive mappings in metric spaces and show that every Osilike-Berinde-G-nonexpansive mapping with nonempty fixed point set is a G-quasinonexpansive mapping. We also prove the demiclosed principle and apply it to obtain a fixed point theorem for Osilike-Berinde-G-nonexpansive mappings. Strong and ∆−convergence theorems of the Ishikawa iteration process for G-quasinonexpansive mappings are also discussed.