Expanding the Applicability of Stirling’s Method under Weaker Conditions and Restricted Convergence Regions-Reference-Cited by-同舟云学术

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

Published:2018-07-01 Issue:1 Volume:56 Page:86-98
ISSN:1841-3307
Container-title:Annals of West University of Timisoara - Mathematics and Computer Science
language:en
Short-container-title:

Author:

Argyros Ioannis K.¹,Parida P.K.²

Affiliation:

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

2. Center for Applied Mathematics , Central University of Jharkhand , Ranchi , India

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/awutm-2018-0007

Reference19 articles.

1. [1] I. K. Argyros, Stirling’s method and fixed points of nonlinear operator equations in Banach spaces, Bull. Inst. Math. Acad. Sin. (N.S.)23, (1995), 13-20

2. [2] I. K. Argyros, On The Convergence and Application of Stirling’s Method, Applicationes Mathematicae, 30, (2003), 109-119

3. [3] I. K. Argyros, A new iterative method of asymptotic order 1+2$1 + \sqrt 2 $ for the computation of fixed points, Int. J. Comput. Math.82, (2005), 1413-1428

4. [4] I. K. Argyros, Computational Theory of Iterative Methods. Series: Studies in Computational Mathematics, 15, (2007)

5. [5] I. K. Argyros and S. Hilout, Weaker conditions for the convergence of Newton’s method, Journal of Complexity, 28, (2012), 364-387

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