Strong Convergence of Monotone Hybrid Algorithms for Maximal Monotone Mappings and Generalized Nonexpansive Mappings

XML PDF
  • 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

Strong Convergence of Monotone Hybrid Algorithms for Maximal Monotone Mappings and Generalized Nonexpansive Mappings. (2025). Communications in Nonlinear Analysis, 11(1). https://oiccpress.com/cna/article/view/17854

PDF views: 305

Abstract

A class of generalized nonexpansive mappings in Banach spaces is considered and a new monotone hybrid algorithm is presented for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a generalized nonexpansive mapping. Under certain conditions on the associated parameters, a strong convergence result is established. Moreover, the obtained result is applied to prove a strong convergence theorem for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a generalized nonexpansive mapping in a Hilbert space.

Keywords

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