International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 3, Pages 133-142

Global asymptotic stability of inhomogeneous iterates

Yong-Zhuo Chen

Department of Mathematics, Computer Science and Engineering, University of Pittsburgh at Bradford, Bradford 16701, PA, USA

Received 3 January 2001

Copyright © 2002 Yong-Zhuo Chen. 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.


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.