Local convergence of an Ulm-like method under ?-type and restricted convergence domain conditions

Abstract

The local convergence of an Ulm-like method is presented to solve nonlinear equations involving Banach space valued operators. The convergence is obtained using weak ?-type conditions as well as a restricted domain containing the iterates. Moreover, the order of convergence for the Ulm-like method is provided. Numerical examples complete this paper. 2018, International Publications. All rights reserved.