A Picard S∗ iterative algorithm for approximating fixed points of generalized α-nonexpansive mappings

Abstract

In this article, we introduce a new iterative algorithm called Picard-S∗ iterative algorithm. We show that the Picard-S∗ iterative algorithm can be used to approximate fixed points of generalized α-nonexpansive mappings. We discuss the convergence results of generalized α-nonexpansive mappings in the framework of CAT(0) spaces using Picard S∗ iteration process and demiclosed principle for the aforementioned class of mappings in CAT(0) spaces. This is the nonlinear version of some known results that have been demonstrated in Banach spaces. Some useful examples are obtained to illustrate facts. Some known iteration processes are also compared using numerical calculations. Our results broaden and improve the corresponding recent results announced by many authors.