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

Document Type : Original Article

Authors

Ioannis K. Argyros ¹

Santhosh George ²

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.

10.22034/kjm.2017.51873

Abstract

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.

Keywords

Chebyshev-Halley method

Banach space

local convergence

radius of convergence

Fréchet-derivative

Subjects

• 46 Functional analysis
• 65 Numerical analysis

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