Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 535849, 11 pages
doi:10.1155/2009/535849
Research Article

Advanced Discrete Halanay-Type Inequalities: Stability of Difference Equations

Ravi P. Agarwal,1 Young-Ho Kim,2 and S. K. Sen1

1Department of Mathematical Sciences, Florida Institute of Technology, 150 West University Boulevard, Melbourne, FL 32901-6975, USA
2Department of Applied Mathematics, Changwon National University, Changwon, Kyeong-Nam 641-773, South Korea

Received 7 December 2008; Accepted 21 January 2009

Academic Editor: Martin J. Bohner

Copyright © 2009 Ravi P. Agarwal 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 derive new nonlinear discrete analogue of the continuous Halanay-type inequality. These inequalities can be used as basic tools in the study of the global asymptotic stability of the equilibrium of certain generalized difference equations.