A new convergence theorem for Steffensen's method on Banach spaces and applications.
Argyros, Ioannis K. (1997)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Argyros, Ioannis K. (1997)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Hernández, M.A., Salanova, M.A. (1997)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Ioannis K. Argyros, Santhosh George (2014)
Applicationes Mathematicae
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We present a local convergence analysis for two popular third order methods of approximating a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for both methods under the same conditions. A comparison is given between the two methods, as well as numerical examples.
Argyros, Ioannis K. (1986)
International Journal of Mathematics and Mathematical Sciences
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Hernández, M.A., Salanova, M.A. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Berinde, V. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Ioannis K. Argyros, Hongmin Ren (2012)
Applicationes Mathematicae
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We provide a semilocal convergence analysis for Halley's method using convex majorants in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our results reduce and improve earlier ones in special cases.
Felix E. Browder (1967)
Mathematische Zeitschrift
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M. Marjanović (1959)
Matematički Vesnik
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Władysław Orlicz, Stanisław Szufla (1981)
Annales Polonici Mathematici
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Santhosh George, Ioannis K. Argyros (2019)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples...
Ioannis K. Argyros, Santhosh George (2015)
Applicationes Mathematicae
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We present a local multi-point convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet derivative. Numerical examples are also provided.
S. Ya. Novikov (1997)
Collectanea Mathematica
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