Discrete Dynamics in Nature and Society 
Volume 2007 (2007), Article ID 10840, 12 pages
doi:10.1155/2007/10840
Research Article

Perron-Type Criterion for Linear Difference Equations with Distributed Delay

Jehad O. Alzabut1,2 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
Received 10 April 2007; Revised 6 July 2007; Accepted 17 August 2007

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.