A monotone hybrid algorithm for maximal monotone operators and a family of generalized nonexpansive mappings

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  • Mathew Aibinu1,
  1. Institute for Systems Science & KZN e-Skills CoLab, Durban University of Technology, Durban 4000, South Africa. DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa. National Institute for Theoretical and Computational Sciences (NITheCS), South Africa

Published in Issue 2025-11-09

How to Cite

A monotone hybrid algorithm for maximal monotone operators and a family of generalized nonexpansive mappings. (2025). Communications in Nonlinear Analysis, 11(2). https://oiccpress.com/cna/article/view/17865

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Abstract

In this paper, a new monotone hybrid method is introduced in the framework of Banach spaces for finding a common element of the set of zeros of a maximum monotone operator and the fixed point set of a family of generalized nonexpansive mappings. The prove is given in the framework of Banach spaces for the strong convergence of a sequence of iteration to a common element of the set of zeros of a maximum monotone operator and the fixed point set of a family of generalized nonexpansive mappings. New convergence results are obtained for resolvents of maximal monotone operators and a family of generalized nonexpansive mappings in a Banach space.

Keywords

  • Generalized,
  • Maximal monotone,
  • Nonexpansive,
  • Retraction,
  • Algorithm
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