MATHEMATICA BOHEMICA, Vol. 133, No. 3, pp. 225-239 (2008)

On the rational recursive sequence $ x_{n+1}=\Big( A+\sum_{i=0}^{k}\alpha_{i}x_{n-i}\Big) \Big/ \sum_{i=0}^{k}\beta_{i}x_{n-i} $

E. M. E. Zayed, M. A. El-Moneam

E. M. E. Zayed, Mathematics Department, Faculty of Science, Taif University, El-Taif, Hawai, P.O. Box 888, Kingdom of Saudi Arabia, e-mail:; M. A. El-Moneam, Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt, e-mail:

Abstract: The main objective of this paper is to study the boundedness character, the periodic character, the convergence and the global stability of positive solutions of the difference equation
x_{n+1}=\bigg( A+\sum_{i=0}^{k}\alpha_{i}x_{n-i}\bigg) \Big/ \sum_{i=0}^{k}\beta_{i}x_{n-i}, n=0,1,2,\dots
where the coefficients $A$, $\alpha_{i}$, $\beta_{i}$ and the initial conditions $x_{-k},x_{-k+1},\dots,x_{-1},x_{0}$ are positive real numbers, while $k$ is a positive integer number.

Keywords: difference equations, boundedness character, period two solution, convergence, global stability

Classification (MSC2000): 39A10, 39A11, 39A99, 34C99

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