IJPAM: Volume 28, No. 3 (2006)

A WEAKER VERSION OF THE SHADOWING LEMMA
FOR OPERATORS WITH CHAOTIC BEHAVIOUR

Ioannis K. Argyros
Department of Mathematical Sciences
Cameron University
Lawton, OK 73505, USA
e-mail: iargyros@cameron.edu


Abstract.We show that it is possible under the same computational cost and weaker hypotheses to find solutions of discrete dynamical systems involving operators with chaotic behaviour.

In particular we weaken the Shadowing Lemma [#!4!#] using a weaker version of the Newton-Kantorovich Theorem, see [#!3!#], recently reported by us in [#!1!#], [#!2!#].

Received: April 19, 2006

AMS Subject Classification: 58F13, 65G99, 47H17, 49M15

Key Words and Phrases: discrete dynamical systems, Newton's method, Banach space, pseudo-orbits, shadowing orbits, Newton-Kantorovich hypothesis, Fréchet derivative, Shadowing Lemma

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 28
Issue: 3