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On nonautonomous discrete dynamical systems driven by means

Advances in Difference Equations volume 2006, Article number: 043470 (2006) Cite this article

Abstract

We investigate the asymptotic behavior of nonautonomous discrete dynamical systems governed by the system of difference equations (recursive equations): y j (n+1) = F j (n,y,(n)); j = 1,...,k, n = 0,1,2,..., where y(n) = (y1(n),...,y k (n)) ∈ ℝk, y(0) = x, and F j (n,·) is a mean of k (≥ 2) positive real numbers, that is, a real-valued function satisfying the internality property min(x) ≤ F j (n,x) ≤ max(x).

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References

  1. Abu-Saris RM: Asymptotic behavior of discrete processes driven by means. Nonlinear Analysis 2004,59(1–2):245–251.

    Article  MathSciNet  MATH  Google Scholar 

  2. Abu-Saris RM, Hajja M: Quadratic means. Journal of Mathematical Analysis and Applications 2003,288(1):299–313. 10.1016/j.jmaa.2003.08.014

    Article  MathSciNet  MATH  Google Scholar 

  3. Borwein JM, Borwein PB: Pi and the AGM, Canadian Mathematical Society Series of Monographs and Advanced Texts. Volume 4. John Wiley & Sons, New York; 1998:xvi+414.

    Google Scholar 

  4. Bullen PS: Handbook of Means and Their Inequalities, Mathematics and Its Applications. Volume 560. Kluwer Academic, Dordrecht; 2003:xxviii+537.

    Book  MATH  Google Scholar 

  5. Cheney W: Analysis for Applied Mathematics, Graduate Texts in Mathematics. Volume 208. Springer, New York; 2001:viii+444.

    MATH  Google Scholar 

  6. Elaydi SN: Nonautonomous difference equations: open problems and conjectures. In Differences and Differential Equations, Fields Inst. Commun.. Volume 42. American Mathematical Society, Rhode Island; 2004:423–428.

    Google Scholar 

  7. Horn RA, Johnson CR: Matrix Analysis. Cambridge University Press, Cambridge; 1985:xiii+561.

    Book  MATH  Google Scholar 

  8. Kempf R: On Ω -limit sets of discrete-time dynamical systems. Journal of Difference Equations and Applications 2002,8(12):1121–1131. 10.1080/10236190290029024

    Article  MathSciNet  MATH  Google Scholar 

  9. Matkowski J: Iterations of mean-type mappings and invariant means. Annales Mathematicae Silesianae 1999, (13):211–226.

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Authors and Affiliations

  1. Department of Basic Sciences, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates

    Raghib M Abu-Saris

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  1. Raghib M Abu-Saris
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Correspondence to Raghib M Abu-Saris.

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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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Abu-Saris, R.M. On nonautonomous discrete dynamical systems driven by means. Adv Differ Equ 2006, 043470 (2006). https://doi.org/10.1155/ADE/2006/43470

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  • DOI: https://doi.org/10.1155/ADE/2006/43470

Keywords

  • Differential Equation
  • Dynamical System
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis