International Journal of Nonlinear Analysis and Applications

Convergence theorems by monotone hybrid algorithms for a family of generalized nonexpansive mappings and maximal monotone operators

Document Type : Research Paper

Authors

1 Institute for Systems Science and KZN e-Skills CoLab, Durban University of Technology, South Africa

2 DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa

3 Department of Applied Mathematics and School for Data Science and Computational Thinking, Stellenbosch University, South Africa

4 National Institute for Theoretical and Computational Sciences (NITheCS), South Africa

Abstract

Finding a zero of a maximal monotone operator is known as one of the most impressive problems which are associated with convex analysis and mathematical optimization. Akin to this is solving the fixed point problems of the class of nonexpansive mappings, which constitutes an important part of nonlinear operators with fascinating applications in several areas such as signal processing and image restoration. This study presents a monotone hybrid algorithm for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a family of a generalized nonexpansive mapping in a Banach space. Suitable conditions under which the algorithm converges strongly are established.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 6
June 2023
Pages 357-369
  • Receive Date: 13 January 2023
  • Revise Date: 17 February 2023
  • Accept Date: 19 March 2023