A note on three-step iterative method for nonlinear equations

Noor and Noor [M.A. Noor, K.I. Noor, Three-step iterative methods for nonlinear equations, Appl. Math. Comput. 183 (2006) 322–327] proposed a three-step iterative method for solving nonlinear equations, and they showed that the method has third-order convergence. In this paper, we propose a new three-step iterative method for solving nonlinear equations, which is a significant improvement of the method proposed by Noor and Noor. It is shown that this iterative method has fourth-order convergence, not third-order convergence. Some numerical experiments are given to illustrate the performance of the three-step iterative method.