Document Type : Research Paper

Author

• Nazlı Karaca

Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, Turkey

Abstract

In this work, we first introduce the modified S-iteration method to approximate common fixed points of three multi-valued generalized $( \alpha -\beta )$-nonexpansive mappings in the setting of Banach spaces. Then we prove some convergence theorems for these mappings by using it. Also, a numerical example is given to illustrate the main results. Furthermore, we introduce a one-step iterative process for generalized $( \alpha -\beta )$-nonexpansive mappings and we prove strong convergence results for the one-step iterative process involving such mappings. Thus our results extend and generalise corresponding results in the contemporary literature.

Keywords

• fixed point
• multi-valued generalized (α-β)-nonexpansive mappings
• uniformly convex Banach space