[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7858/eamj.2011.27.5.521

EXTENDING THE APPLICATION OF THE SHADOWING LEMMA FOR OPERATORS WITH CHAOTIC BEHAVIOUR

Argyros, Ioannis K. (Cameron university, Department of Mathematics Sciences)

Publication Information

East Asian mathematical journal / v.27, no.5, 2011 , pp. 521-525 More about this Journal

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;

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