Advances in Difference Equations
Volume 2006 (2006), Article ID 43470, 7 pages
doi:10.1155/ADE/2006/43470
On nonautonomous discrete dynamical systems driven by means
Department of Basic Sciences, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates
Received 27 March 2006; Revised 13 June 2006; Accepted 14 June 2006
Copyright © 2006 Raghib M. Abu-Saris. 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.
Abstract
We investigate the asymptotic behavior of nonautonomous discrete
dynamical systems governed by the system of difference equations
(recursive equations): yj(n+1)=Fj(n,y(n)); j=1,…,k,n=0,1,2,…, where y(n)=(y1(n),…,yk(n))∈ℝk, y(0)=x, and Fj(n,⋅) is a mean of k (≥2) positive real numbers, that is, a real-valued function satisfying the
internality property min(x)≤Fj(n,x)≤max(x).