Convergence results of a faster iterative scheme including multi-valued mappings in Banach spaces

Abstract

In this paper, we study three-step iterative scheme of Ullah and Arshad so-called $M$-iterative scheme in the new context of multi-valued generalized $\alpha$-nonexpansive mappings. A uniformly convex Banach space is used as underlying setting for our approach. We also provide a new example of generalized $\alpha$-nonexpasive mappings. We connect $M$ iterative scheme and other well known schemes with this example, to show the numerical efficiency of our results. Our results improve and extend to many existing results o the current literature.