A monotone hybrid algorithm for a family of generalized nonexpansive mappings in Banach spaces

Document Type : Research Paper

Authors

1 Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran

2 Department of Mathematics, Sahand University of Technology, Tabriz, Iran

Abstract

In this paper, we propose a new monotone hybrid method for getting a common fixed point of a family of generalized nonexpansive mappings and prove a  strong convergence theorem for this family in the framework of Banach spaces. Using this theorem, we obtain some new results for the class of generalized nonexpansive mappings and finitely many generalized nonexpansive mappings. Using the FMINCON optimization toolbox in MATLAB, we give a numerical example to illustrate the usability of our results.

Keywords

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Volume 13, Issue 2
July 2022
Pages 2347-2359
  • Receive Date: 23 July 2019
  • Revise Date: 11 September 2021
  • Accept Date: 20 September 2021