International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 3, Pages 133-142
Global asymptotic stability of inhomogeneous iterates
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 be a finite-dimensional complete metric space, and a sequence of uniformly convergent operators on
. We study the non-autonomous discrete dynamical system
and the globally asymptotic stability of the
inhomogeneous iterates of . Then we apply the results
to investigate the stability of equilibrium of 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.