Convergence Analysis of a Fifth-Order Iterative Method Using Recurrence Relations and Conditions on the First Derivative

Abstract

Using conditions on the second Fréchet derivative, fifth order of convergence was established in Singh et al. (Mediterr J Math 13:4219–4235, 2016) for an iterative method. In this paper, we establish fifth order of convergence of the method using assumptions only on the first Fréchet derivative of the involved operator. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.