Extending the applicability of the super-Halley-like method using ω-continuous derivatives and restricted convergence domains

Joannis K. Argyros; Santhosh George

Published: 2018-10-27

Vol. 33 (2019)

Extending the applicability of the super-Halley-like method using ω-continuous derivatives and restricted convergence domains

Joannis K. Argyros , Santhosh George

Abstract

We present a local convergence analysis of the 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 studies 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 up to the second derivative. We also provide: a computable error on the distances involved and a uniqueness result based on Lipschitz constants. Numerical examples are also presented in this study.

Keywords:

super-Halley-like method , Banach space , local convergence , Fréchet derivative

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Argyros, J. K., & George, S. (2018). Extending the applicability of the super-Halley-like method using ω-continuous derivatives and restricted convergence domains. Annales Mathematicae Silesianae, 33, 21–40. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13648

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Joannis K. Argyros

Affiliation:

Department of Mathematical Sciences, Cameron University, USA United States

Santhosh George

sgeorge@nitk.edu.in

Affiliation:

Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India India

Vol. 33 (2019)
Published: 2019-07-18

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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