Extending the applicability of an Ulm-Newton-like method under generalized conditions in Banach space

Argyros, I.K.George, S.2026-02-052020Transactions of A. Razmadze Mathematical Institute, 2020, 174, 1, pp. 15-2223468092https://idr.nitk.ac.in/handle/123456789/24113The aim of this paper is to extend the applicability of an Ulm-Newton-like method for approximating a solution of a nonlinear equation in a Banach space setting. The sufficient local convergence conditions are weaker than those in the earlier works leading to a larger radius of convergence and more precise error estimations on the distances involved. Numerical examples are also provided. © 2020 A. Razmadze Mathematical Institute of Iv. Javakhishvili Tbilisi State University. All rights reserved.Banach spaceLocal/semi-local convergenceUlm's methodExtending the applicability of an Ulm-Newton-like method under generalized conditions in Banach space