Unified Convergence for Multi-Point Super Halley-Type Methods with Parameters in Banach Space

Ioannis K. Argyros () and Santhosh George ()
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Ioannis K. Argyros: Cameron University
Santhosh George: National Institute of Technology Karnataka

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 1, 1-13

Abstract: Abstract We present a local convergence analysis of a multi-point super-Halley-like method in order to approximate a locally unique solution of an equation in a Banach space setting. The convergence analysis in earlier works was based on hypotheses reaching up to the third derivative of the operator. In the present study we expand the applicability of the Super-Halley-like method by using hypotheses only on the first derivative. We also provide: A computable error on the distances involved and a uniqueness result based on Lipschitz constants. The convergence order is also provided for these methods. Numerical examples are also presented in this study.

Keywords: Halley-type method; Newton’s methods; Banach space; local convergence (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0302-2

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