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

Abstract

The 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.