Convergence of the S-iteration process for the multi-valued generalized $( \alpha -\beta )$-nonexpansive mappings in Banach spaces

Document Type : Research Paper


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


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.


Volume 14, Issue 1
January 2023
Pages 2007-2018
  • Receive Date: 02 January 2022
  • Revise Date: 23 November 2022
  • Accept Date: 26 November 2022