Gheondea, A.Şamcı, M. E.2018-04-122018-04-1220170025-584Xhttp://hdl.handle.net/11693/36409We provide an answer to a question raised by S. Amat, S. Busquier, S. Plaza on the qualitative analysis of the dynamics of a certain third order Newton type approximation function Mf, by proving that for functions f twice continuously differentiable and such that both f and its derivative do not have multiple roots, with at least four roots and infinite limits of opposite signs at ±∞, Mf has periodic points of any prime period and that the set of points a at which the approximation sequence (Mn f(a))n ∈ ℕ does not converge is uncountable. In addition, we observe that in their Scaling Theorem analyticity can be replaced with differentiability. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimEnglish37E15chaosNewton’s approximation methodperiodic pointsPrimary: 37N30Secondary: 37D45third orderArticle10.1002/mana.2015004701522-2616