Document Type : Original Article
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA.
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025.
We present a local convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet-derivative. Numerical examples are also provided in this study.