International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 3, Pages 133-142
doi:10.1155/S0161171202011316
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
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.