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

Abstract

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,.

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References

  1. 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.1999.6384

    MathSciNet  Article  MATH  Google Scholar 

  2. 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.2005.09.049

    MathSciNet  Article  MATH  Google Scholar 

  3. 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/j.na.2005.06.005

    MathSciNet  Article  MATH  Google Scholar 

  4. 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. 10.1080/10236199908808204

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Nesemann T: Positive nonlinear difference equations: some results and applications. Nonlinear Analysis 2001,47(7):4707–4717. 10.1016/S0362-546X(01)00583-1

    MathSciNet  Article  MATH  Google Scholar 

  6. 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.2004.02.039

    MathSciNet  Article  MATH  Google Scholar 

  7. 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.2004.11.040

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Kuang J: Applied Inequalities. Shandong Science and Technology Press, Jinan, China; 2004.

    Google Scholar 

  9. 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.

    Google Scholar 

  10. 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.

    Google Scholar 

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Correspondence to Xiaofan Yang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Yang, X., Yang, M. & Liu, H. A Part-Metric-Related Inequality Chain and Application to the Stability Analysis of Difference Equation. J Inequal Appl 2007, 019618 (2007). https://doi.org/10.1155/2007/19618

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Keywords

  • Stability Analysis
  • Difference Equation
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