A one-parameter fourth-order family of iterative methods for nonlinear equations Changbum Chun a, * , YoonMee Ham b a School of Liberal Arts, Korea University of Technology and Education, Cheonan, Chungnam 330-708, Republic of Korea b Department of Mathematics, Kyonggi University, Suwon 442-760, Republic of Korea Abstract In this paper, we present a new one-parameter fourth-order family of iterative methods for solving nonlinear equations. The new family requires two evaluations of the given function and one of its first derivative per iteration. The well-known Traub–Ostrowski’s fourth-order method is shown to be part of the family. Several numerical examples are given to illus- trate the efficiency and performance of the presented methods. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Newton’s method; Iterative methods; Nonlinear equations; Order of convergence 1. Introduction In this paper, we consider iterative methods to find a simple root a, i.e., f ðaÞ¼ 0 and f 0 ðaÞ 6¼ 0, of a non- linear equation f ðxÞ¼ 0. Newton’s method is the well-known iterative method for finding a by using x nþ1 ¼ x n  f ðx n Þ f 0 ðx n Þ ð1Þ that converges quadratically in some neighborhood of a [1]. In recent years, some fourth-order iterative methods have been proposed and analyzed for solving nonlin- ear equations that improve several classical methods such as Newton’s method, Halley-like methods, etc., and do require three evaluations of the given function and its first derivative per iteration, see [2–7] and the refer- ence therein. It has been shown that these methods are efficient in their performance, can compete with Newton’s method as well as classical fourth-order methods such as Jarratt’s method and Traub–Ostrowski’ method. 0096-3003/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2006.11.113 * Corresponding author. E-mail addresses: cbchun@kut.ac.kr (C. Chun), ymham@kyonggi.ac.kr (Y. Ham). Applied Mathematics and Computation 189 (2007) 610–614 www.elsevier.com/locate/amc