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Vol. 49 No. 4 (2023)
Serdica Mathematical Journal

Articles

Newton's method for generalized equations under weak conditions

https://doi.org/10.55630/serdica.2023.49.269-282

Published 21-12-2023

  • Ioannis K. Argyros
    • ,
  • Santhosh George

Ioannis K. Argyros
Cameron University, USA

Santhosh George
National Institute of Technology Karnataka

Abstract

A local convergence analysis is developed for Newton’s method in order to approximate a solution of a generalized equations in a Banach space setting. The convergence conditions are based on generalized continuity conditions on the Fr´echet derivative of the operator involved and the Aubin property. The specialized cases of our results extend earlier ones using similar information.

2020 Mathematics Subject Classification:

34A34, 65B99, 65P30, 65H05

Keywords

Banach space, local convergence, Newton's method, generalized equation

Full text

Author Details

Ioannis K. Argyros

Department of Mathematical Sciences
Cameron University
Lawton, OK 73505, USA
e-mail:  iargyros@cameron.edu

Santhosh George

Department of Mathematical and Computational Sciences
National Institute of Technology Karnataka
India-575 025
e-mail: sgeorge@nitk.edu.in

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