Extending the radius of convergence for a class of Euler-Halley type methods

Abstract

The aim of this paper is to extend the radius of convergence and improve the ratio of convergence for a certain class of Euler-Halley type methods with one parameter in a Banach space. These improvements over earlier works are obtained using the same functions as before but more precise information on the location of the iterates. Special cases and examples are also presented in this study.