<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Department of Mathematical and Computational Sciences

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

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...

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

Published Online: Jul 18, 2019

Page range: 21 - 40

Received: Oct 09, 2017

Accepted: Aug 25, 2018

DOI: https://doi.org/10.2478/amsil-2018-0008

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

© 2019 Ioannis K. Argyros et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Jul 18, 2019

Page range: 21 - 40

Received: Oct 09, 2017

Accepted: Aug 25, 2018

DOI: https://doi.org/10.2478/amsil-2018-0008

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

© 2019 Ioannis K. Argyros et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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