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Mathematics 2019, 7(1), 89; https://doi.org/10.3390/math7010089

Ball Comparison for Some Efficient Fourth Order Iterative Methods Under Weak Conditions

1
Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
2
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 17 December 2018 / Revised: 5 January 2019 / Accepted: 9 January 2019 / Published: 16 January 2019
(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems)
Full-Text   |   PDF [286 KB, uploaded 16 January 2019]

Abstract

We provide a ball comparison between some 4-order methods to solve nonlinear equations involving Banach space valued operators. We only use hypotheses on the first derivative, as compared to the earlier works where they considered conditions reaching up to 5-order derivative, although these derivatives do not appear in the methods. Hence, we expand the applicability of them. Numerical experiments are used to compare the radii of convergence of these methods. View Full-Text
Keywords: fourth order iterative methods; local convergence; banach space; radius of convergence fourth order iterative methods; local convergence; banach space; radius of convergence
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Argyros, I.K.; Behl, R. Ball Comparison for Some Efficient Fourth Order Iterative Methods Under Weak Conditions. Mathematics 2019, 7, 89.

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