International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 7, Pages 1007-1013
doi:10.1155/IJMMS.2005.1007

A note on asymptotic stability conditions for delay difference equations

T. Kaewong,1 Y. Lenbury,2 and P. Niamsup1

1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2Department of Mathematics, Faculty of Science, Mahidol University, 272 Rama 6 Road, Bangkok 10400, Thailand

Received 26 May 2004; Revised 27 February 2005

Copyright © 2005 T. Kaewong et al. 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 obtain necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation xn+1+p∑j=1Nxn−k+(j−1)l=0, where n=0,1,2,…, is a real number, and k, l, and N are positive integers such that k>(N−1)l.