Ball convergence of a novel bi-parametric iterative scheme for solving equations

Abstract

The aim of this article is to establish a ball convergence result for a bi-parametric iterative scheme for solving equations involving Banach space-valued operators. In contrast to earlier approaches in the less general setting of the k-dimensional Eu-clidean space where hypotheses on the seventh derivative are used, while we only use hypotheses on the first derivative. Hence, we extend the applicability of the method. Moreover, the radius of convergence as well as error bounds on the distances are given based on Lipschitz-type functions. Numerical examples are given to test our conditions. These examples show that earlier convergence conditions are not satisfied but ours are satisfied. © 2020, International Publications. All rights reserved.