Generic properties of infinite system of integral equations in Banach spaces
Władysław Orlicz, Stanisław Szufla (1981)
Annales Polonici Mathematici
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Władysław Orlicz, Stanisław Szufla (1981)
Annales Polonici Mathematici
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M. Marjanović (1959)
Matematički Vesnik
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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.
Hernández, M.A., Salanova, M.A. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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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...
A. C. Babu (1982)
Publications de l'Institut Mathématique
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Hernández, M.A., Salanova, M.A. (1997)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Volodin, A., Antonini, Giuliano R., Hu, T.-C. (2004)
Lobachevskii Journal of Mathematics
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Prasit Cholamjiak, Yekini Shehu (2019)
Applications of Mathematics
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We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the few available inertial-type methods for zeros of the sum of accretive operators in Banach spaces. ...
Argyros, Ioannis K. (1996)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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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.