EXTENDED KANTOROVICH-TYPE RESULTS ON NEWTON’S METHOD FOR SOLVING GENERALIZED EQUATIONS

Dedicated to Professor Constantin Fetecau on the occasion of his 80th anniversary

 

Ioannis K. Argyros†, Santhosh George‡

Abstract: A semi-local convergence analysis is developed for Newton’s method in order to approximate a solution of a generalized equations involving Banach space valued operators. The convergence conditions are based on generalized continuity conditions on the Fréchet derivative of the operator involved and the Aubin property. The specialized cases of our results extend earlier ones using the same information. Suitable examples complement the theory.

Keywords: Banach space, semi-local convergence, Newton’s method, generalized equation.

MSC: 34A34, 65B99, 65P30, 65H05.

DOI 10.56082/annalsarscimath.2026.4.129

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*Accepted for publication on July 17, 2026
†iargyros@cameron.edu, Department of Mathematical Sciences, Cameron University, Lawton, OK 73505
‡sgeorge@nitk.edu.in, Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 4, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997