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. Kaewong1
, Y. Lenbury2
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
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.