Local Convergence for a Family of Sixth Order Chebyshev-Halley-Type Methods in Banach Space Under Weak Conditions

Document Type : Original Article


1 Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA.

2 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.


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