Recurrence Relations for the Super-Halley Method

In this paper we give sufficient conditions in order to assure the convergence of the super-Halley method in Banach spaces. We use a system of recurrence relations analogous to those given in the classical Newton-Kantorovich theorem, or those given for Chebyshev and Halley methods by different authors. (~) 1998 Elsevier Science Ltd. All rights reserved.