A note on “Some higher-order modifications of Newton's method for solving nonlinear equations”

In [YoonMee Ham, Changbum Chun, Sang-Gu Lee, Some higher-order modifications of Newtons method for solving nonlinear equations, J. Comput. Appl. Math., in press, doi:10.1016/j.cam.2007.11.018], a method to construct some higher order modifications of Newton's method has been presented. In this paper, we show that the main result given by the authors is not accurate for p = 1 and p = 2. Some counterexamples are given to verify our analysis.