On the rational recursive sequence $ x_{n+1}=\dfrac{\alpha _0x_n+\alpha _1x_{n-l}+\alpha _2x_{n-k}}{\beta _0x_n+\beta _1x_{n-l}+\beta _2x_{n-k}}$

E. M. E. Zayed; M. A. El-Moneam

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

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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 $x_{n + 1} = (A + \sum_{i = 0}^{k} α_{i} x_{n - i}) / \sum_{i = 0}^{k} β_{i} x_{n - i}, n = 0, 1, 2, \dots$ where the coefficients $A$ , $α_{i}$ , $β_{i}$ 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.

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Displaying similar documents to “On the rational recursive sequence x n + 1 = α 0 x n + α 1 x n - l + α 2 x n - k β 0 x n + β 1 x n - l + β 2 x n - k ”

Displaying similar documents to “On the rational recursive sequence $x_{n + 1} = \frac{α_{0} x_{n} + α_{1} x_{n - l} + α_{2} x_{n - k}}{β_{0} x_{n} + β_{1} x_{n - l} + β_{2} x_{n - k}}$ ”