East Asian mathematical journal
- Volume 27 Issue 5
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- Pages.521-525
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- 2011
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- 1226-6973(pISSN)
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- 2287-2833(eISSN)
DOI QR Code
EXTENDING THE APPLICATION OF THE SHADOWING LEMMA FOR OPERATORS WITH CHAOTIC BEHAVIOUR
- Argyros, Ioannis K. (Cameron university, Department of Mathematics Sciences)
- Received : 2010.02.11
- Accepted : 2011.08.03
- Published : 2011.11.30
Abstract
We use a weaker version of the celebrated Newton-Kantorovich theorem [3] reported by us in [1] to find solutions of discrete dynamical systems involving operators with chaotic behavior. Our results are obtained by extending the application of the shadowing lemma [4], and are given under the same computational cost as before [4]-[6].
Keywords
- discrete dynamical systems;
- Newton's method;
- Banach space;
- pseudo-orbits;
- shadowing orbits;
- Newton-Kantorovich hypothesis;
- Fr$\acute{e}$chet derivative;
- shadowing Lemma