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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.

On the rational recursive sequence $x_{n + 1} = \frac{α_{0} x_{n} + α_{1} x_{n - l} + α_{2} x_{n - k}}{β_{0} x_{n} + β_{1} x_{n - l} + β_{2} x_{n - k}}$

E. M. E. Zayed, M. A. El-Moneam (2010)

Mathematica Bohemica

The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation $x_{n + 1} = \frac{α_{0} x_{n} + α_{1} x_{n - l} + α_{2} x_{n - k}}{β_{0} x_{n} + β_{1} x_{n - l} + β_{2} x_{n - k}}, n = 0, 1, 2, \dots$ where the coefficients $α_{i}, β_{i} \in (0, \infty)$ for $i = 0, 1, 2,$ and $l$ , $k$ are positive integers. The initial conditions $x_{- k}, \dots, x_{- l}, \dots, x_{- 1}, x_{0}$ are arbitrary positive real numbers such that $l < k$ . Some numerical experiments are presented.

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On the max-type difference equation $x_{n + 1} = max {A / x_{n}, x_{n - 3}}$ .

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On the oscillation of the solutions to linear difference equations with variable delay.

On the oscillatory behavior for a certain class of third order nonlinear delay difference equations.

On the periodic nature of some max-type difference equations.

On the periodicity of a difference equation with maximum.

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

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

On the rational recursive sequence $x_{n + 1} = \frac{α_{0} x_{n} + α_{1} x_{n - l} + α_{2} x_{n - k}}{β_{0} x_{n} + β_{1} x_{n - l} + β_{2} x_{n - k}}$

On the rational recursive sequence $x_{n + 1} = (α - β x_{n}) / (γ - δ x_{n} - x_{n - k})$ .

On the recursive sequence.

On the recursive sequence $x_{n + 1} = A + (x_{n - 1}^{p} / x_{n}^{q})$ .

On the recursive sequence $x_{n + 1} = A + x_{n}^{p} / x_{n - 1}^{p}$ .

On the recursive sequence $x_{n + 1} = A + x_{n}^{p} / x_{n - 1}^{r}$ .

On the recursive sequence $x_{n} = 1 + \sum_{i = 1}^{k} α_{i} x_{n - p_{i}} / \sum_{j = 1}^{m} β_{j} x_{n - q_{j}}$ .

Currently displaying 121 – 140 of 233