A Fréchet derivative-free cubically convergent method for set-valued maps |
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Authors: | Ioannis K Argyros Saïd Hilout |
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Institution: | (1) Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA;(2) Laboratoire de Mathématiques et Applications, Poitiers University, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France |
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Abstract: | We introduce a new iterative method in order to approximate a locally unique solution of variational inclusions in Banach
spaces. The method uses only divided differences operators of order one. An existence–convergence theorem and a radius of
convergence are given under some conditions on divided difference operator and Lipschitz-like continuity property of set-valued
mappings. Our method extends the recent work related to the resolution of nonlinear equation in Argyros (J Math Anal Appl
332:97–108, 2007) and has the following advantages: faster convergence to the solution than all the previous known ones in Argyros and Hilout
(Appl Math Comput, 2008 in press), Hilout (J Math Anal Appl 339:53–761, 2008, Positivity 10:673–700, 2006), and we do not need to evaluate any Fréchet derivative. We provide also an improvement of the ratio of our algorithm under
some center-conditions and less computational cost. Numerical examples are also provided.
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Keywords: | Banach space Divided differences operators Generalized equation Aubin’ s continuity Radius of convergence Fréchet derivative Set-valued map |
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