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Open AccessArticle

Ball Convergence for Combined Three-Step Methods Under Generalized Conditions in Banach Space

Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
Author to whom correspondence should be addressed.
Symmetry 2019, 11(8), 1002;
Received: 21 June 2019 / Revised: 23 July 2019 / Accepted: 24 July 2019 / Published: 3 August 2019
(This article belongs to the Special Issue Symmetry with Operator Theory and Equations)
PDF [259 KB, uploaded 3 August 2019]


Problems from numerous disciplines such as applied sciences, scientific computing, applied mathematics, engineering to mention some can be converted to solving an equation. That is why, we suggest higher-order iterative method to solve equations with Banach space valued operators. Researchers used the suppositions involving seventh-order derivative by Chen, S.P. and Qian, Y.H. But, here, we only use suppositions on the first-order derivative and Lipschitz constrains. In addition, we do not only enlarge the applicability region of them but also suggest computable radii. Finally, we consider a good mixture of numerical examples in order to demonstrate the applicability of our results in cases not covered before. View Full-Text
Keywords: local convergence; convergence order; Banach space; iterative method local convergence; convergence order; Banach space; iterative method
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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Alharbey, R.A.; Argyros, I.K.; Behl, R. Ball Convergence for Combined Three-Step Methods Under Generalized Conditions in Banach Space. Symmetry 2019, 11, 1002.

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