Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains-Reference-Cited by-同舟云学术

Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains

Published:2019-07-18 Issue:1 Volume:33 Page:21-40
ISSN:2391-4238
Container-title:Annales Mathematicae Silesianae
language:en
Short-container-title:

Author:

Argyros Ioannis K.¹,George Santhosh²

Affiliation:

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

2. Department of Mathematical and Computational Sciences , National Institute of Technology Karnataka, 575 025 Karnataka , India

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/amsil-2018-0008

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