<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we have provided sufficient conditions to study semilocal and local convergence of the Stirling’s method. The method is used to find fixed points of nonlinear operator equation. We assume Lipschtiz continuity type conditions on the first Fréchet derivative of the operator but no contractive conditions as in earlier works. This way expand the applicability of this method. Here we introduce a new type of majorizing sequences instead of usual majorizing sequences and recurrence relations. Finally the paper will be concluded with numerical examples and a favorable comparison with known results.</p></abstract>

In this paper we have provided sufficient conditions to study semilocal and local convergence of the Stirling’s method. The method is used to find fixed points of nonlinear operator equation. We assume Lipschtiz continuity type conditions on the first Fréchet derivative of the operator but no contractive conditions as in earlier works. This way expand the applicability of this method. Here we introduce a new type of majorizing sequences instead of usual majorizing sequences and recurrence relations. Finally the paper will be concluded with numerical examples and a favorable comparison with known results.

Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper we have provided sufficient conditions to study semilocal and local convergence of the Stirling’s method. The method is used to find fixed points...

Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions

Published Online: Dec 07, 2018

Page range: 86 - 98

Received: Nov 10, 2017

Accepted: Jan 10, 2018

DOI: https://doi.org/10.2478/awutm-2018-0007

Keywords
Stirling’s method, Lipschtiz continuity condition, Majorizing sequences, Semilocal convergence, Local convergence, Computable radius of convergence

© 2018 Ioannis K. Argyros et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions

Published Online: Dec 07, 2018

Page range: 86 - 98

Received: Nov 10, 2017

Accepted: Jan 10, 2018

DOI: https://doi.org/10.2478/awutm-2018-0007

KeywordsStirling’s method, Lipschtiz continuity condition, Majorizing sequences, Semilocal convergence, Local convergence, Computable radius of convergence

© 2018 Ioannis K. Argyros et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Stirling’s method, Lipschtiz continuity condition, Majorizing sequences, Semilocal convergence, Local convergence, Computable radius of convergence