On nonautonomous discrete dynamical systems driven by means
© Raghib M. Abu-Saris 2006
Received: 27 March 2006
Accepted: 14 June 2006
Published: 27 September 2006
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)) ∈ ℝ 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).
- Abu-Saris RM: Asymptotic behavior of discrete processes driven by means. Nonlinear Analysis 2004,59(1–2):245–251.MathSciNetView ArticleMATHGoogle Scholar
- Abu-Saris RM, Hajja M: Quadratic means. Journal of Mathematical Analysis and Applications 2003,288(1):299–313. 10.1016/j.jmaa.2003.08.014MathSciNetView ArticleMATHGoogle Scholar
- 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
- Bullen PS: Handbook of Means and Their Inequalities, Mathematics and Its Applications. Volume 560. Kluwer Academic, Dordrecht; 2003:xxviii+537.View ArticleMATHGoogle Scholar
- Cheney W: Analysis for Applied Mathematics, Graduate Texts in Mathematics. Volume 208. Springer, New York; 2001:viii+444.MATHGoogle Scholar
- 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
- Horn RA, Johnson CR: Matrix Analysis. Cambridge University Press, Cambridge; 1985:xiii+561.View ArticleMATHGoogle Scholar
- Kempf R: On Ω -limit sets of discrete-time dynamical systems. Journal of Difference Equations and Applications 2002,8(12):1121–1131. 10.1080/10236190290029024MathSciNetView ArticleMATHGoogle Scholar
- Matkowski J: Iterations of mean-type mappings and invariant means. Annales Mathematicae Silesianae 1999, (13):211–226.
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