Argyros, I.K.George, S.2026-02-042023Serdica Mathematical Journal, 2023, 49, 4, pp. 269-28213106600https://doi.org/10.55630/serdica.2023.49.269-282https://idr.nitk.ac.in/handle/123456789/21544A 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 Fréchet derivative of the operator involved and the Aubin property. The specialized cases of our results extend earlier ones using similar information. © 2023, Bulgarian Academy of Sciences, Institute of Mathematics and Informatics. All rights reserved.Banach spacegeneralized equationlocal convergenceNewton’s method