Open Access

A Part-Metric-Related Inequality Chain and Application to the Stability Analysis of Difference Equation

Journal of Inequalities and Applications20072007:019618

DOI: 10.1155/2007/19618

Received: 8 October 2006

Accepted: 14 December 2006

Published: 20 March 2007


We find a new part-metric-related inequality of the form , where . We then apply this result to show that is a globally asymptotically stable equilibrium of the rational difference equation , .


Authors’ Affiliations

College of Computer Science, Chongqing University


  1. Kruse N, Nesemann T: Global asymptotic stability in some discrete dynamical systems. Journal of Mathematical Analysis and Applications 1999,235(1):151–158. 10.1006/jmaa.1999.6384MathSciNetView ArticleMATHGoogle Scholar
  2. Yang X: Global asymptotic stability in a class of generalized Putnam equations. Journal of Mathematical Analysis and Applications 2006,322(2):693–698. 10.1016/j.jmaa.2005.09.049MathSciNetView ArticleMATHGoogle Scholar
  3. Yang X, Evans DJ, Megson GM: Global asymptotic stability in a class of Putnam-type equations. Nonlinear Analysis 2006,64(1):42–50. 10.1016/ ArticleMATHGoogle Scholar
  4. Amleh AM, Kruse N, Ladas G: On a class of difference equations with strong negative feedback. Journal of Difference Equations and Applications 1999,5(6):497–515. 10.1080/10236199908808204MathSciNetView ArticleMATHGoogle Scholar
  5. Nesemann T: Positive nonlinear difference equations: some results and applications. Nonlinear Analysis 2001,47(7):4707–4717. 10.1016/S0362-546X(01)00583-1MathSciNetView ArticleMATHGoogle Scholar
  6. Papaschinopoulos G, Schinas CJ: Global asymptotic stability and oscillation of a family of difference equations. Journal of Mathematical Analysis and Applications 2004,294(2):614–620. 10.1016/j.jmaa.2004.02.039MathSciNetView ArticleMATHGoogle Scholar
  7. Sun T, Xi H: Global asymptotic stability of a family of difference equations. Journal of Mathematical Analysis and Applications 2005,309(2):724–728. 10.1016/j.jmaa.2004.11.040MathSciNetView ArticleMATHGoogle Scholar
  8. Kuang J: Applied Inequalities. Shandong Science and Technology Press, Jinan, China; 2004.Google Scholar
  9. Kocić VL, Ladas G: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Mathematics and Its Applications. Volume 256. Kluwer Academic Publishers, Dordrecht, The Netherlands; 1993:xii+228.MATHGoogle Scholar
  10. Kulenović MRS, Ladas G: Dynamics of Second Order Rational Difference Equations, with Open Problems and Conjectures. Chapman & Hall/CRC Press, Boca Raton, Fla, USA; 2002:xii+218.MATHGoogle Scholar


© Xiaofan Yang et al. 2007

This article is published under license to BioMed Central Ltd. 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.