Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 10840, 12 pages
doi:10.1155/2007/10840
Perron-type criterion for linear difference equations with distributed delay
Jehad O. Alzabut1
and Thabet Abdeljawad2
1Department of Mathematics, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
2Department of Mathematics and Computer Science, Çankaya University, Ankara 06530, Turkey
Abstract
It is shown that if a linear difference equation with distributed delay of the form Δx(n)=∑k=−d0Δkζ(n+1,k−1)x(n+k−1), n≥1, satisfies a Perron condition then its trivial solution is uniformly asymptotically stable.