A unifying theorem for Newton’s method on spaces with a convergence structure |
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| Authors: | Ioannis K. Argyros |
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| Affiliation: | a Cameron University, Department of Mathematics Sciences, Lawton, OK 73505, USAb Poitiers University, Laboratoire de Mathématiques et Applications, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France |
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| Abstract: | We present a semilocal convergence theorem for Newton’s method (NM) on spaces with a convergence structure. Using our new idea of recurrent functions, we provide a tighter analysis, with weaker hypotheses than before and with the same computational cost as for Argyros (1996, 1997, 1997, 2007) [1], [2], [3] and [5], Meyer (1984, 1987, 1992) [13], [14] and [15]. Numerical examples are provided for solving equations in cases not covered before. |
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| Keywords: | Newton&rsquo s method Banach space Convergence structure Fixed point Kantorovich hypothesis |
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