Skip to main content

Theory and Modern Applications

  • Research Article
  • Open access
  • Published:

On nonautonomous discrete dynamical systems driven by means


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)) k, 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).



  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.

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Raghib M Abu-Saris.

Rights and permissions

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

Reprints and permissions

About this article

Cite this article

Abu-Saris, R.M. On nonautonomous discrete dynamical systems driven by means. Adv Differ Equ 2006, 043470 (2006).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: