International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2002 / Article

Open Access

Volume 29 |Article ID 513109 | 10 pages | https://doi.org/10.1155/S0161171202011316

Global asymptotic stability of inhomogeneous iterates

Received03 Jan 2001

Abstract

Let (M,d) be a finite-dimensional complete metric space, and {Tn} a sequence of uniformly convergent operators on M. We study the non-autonomous discrete dynamical system xn+1=Tnxn and the globally asymptotic stability of the inhomogeneous iterates of {Tn}. Then we apply the results to investigate the stability of equilibrium of T when it satisfies certain type of sublinear conditions with respect to the partial order defined by a closed convex cone. The examples of application to nonlinear difference equations are also given.

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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