On solutions of the difference equation $x_{n+1}=x_{n-3}/(-1+x_{n}x_{n-1}x_{n-2}x_{n-3})$

Cengiz Cinar; Ramazan Karatas; Ibrahim Yalçınkaya

Displaying similar documents to “On solutions of the difference equation $x_{n + 1} = x_{n - 3} / (- 1 + x_{n} x_{n - 1} x_{n - 2} x_{n - 3})$ ”

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

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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.

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

E. M. E. Zayed, M. A. El-Moneam (2008)

Mathematica Bohemica

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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.

Expressions of solutions for a class of differential equations.

Elsayed, E.M. (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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On the difference equation $x_{n + 1} = \frac{a_{0} x_{n} + a_{1} x_{n - 1} + \dots + a_{k} x_{n - k}}{b_{0} x_{n} + b_{1} x_{n - 1} + \dots + b_{k} x_{n - k}}$

Elmetwally M. Elabbasy, Hamdy El-Metwally, E. M. Elsayed (2008)

Mathematica Bohemica

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In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence $x_{n + 1} = \frac{a_{0} x_{n} + a_{1} x_{n - 1} + \dots + a_{k} x_{n - k}}{b_{0} x_{n} + b_{1} x_{n - 1} + \dots + b_{k} x_{n - k}}, n = 0, 1, \dots$ where the parameters $a_{i}$ and $b_{i}$ for $i = 0, 1, \dots, k$ are positive real numbers and the initial conditions $x_{- k}, x_{- k + 1}, \dots, x_{0}$ are arbitrary positive numbers.

On the recursive sequence.

Camouzis, E., Devault, R., Papaschinopoulos, G. (2005)

Advances in Difference Equations [electronic only]

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On boundedness of solutions of the difference equation $x_{n + 1} = (p x_{n} + q x_{n - 1}) / (1 + x_{n})$ for $q > 1 + p > 1$ .

Xi, Hongjian, Sun, Taixiang, Yu, Weiyong, Zhao, Jinfeng (2009)

Advances in Difference Equations [electronic only]

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Displaying similar documents to “On solutions of the difference equation x n + 1 = x n - 3 / ( - 1 + x n x n - 1 x n - 2 x n - 3 ) ”

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

On the rational recursive sequence x n + 1 = A + ∑ i = 0 k α i x n - i / ∑ i = 0 k β i x n - i

Expressions of solutions for a class of differential equations.

On the difference equation x n + 1 = a 0 x n + a 1 x n - 1 + ⋯ + a k x n - k b 0 x n + b 1 x n - 1 + ⋯ + b k x n - k

On the recursive sequence.

On boundedness of solutions of the difference equation x n + 1 = ( p x n + q x n - 1 ) / ( 1 + x n ) for q > 1 + p > 1 .

Displaying similar documents to “On solutions of the difference equation $x_{n + 1} = x_{n - 3} / (- 1 + x_{n} x_{n - 1} x_{n - 2} x_{n - 3})$ ”

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

On the difference equation $x_{n + 1} = \frac{a_{0} x_{n} + a_{1} x_{n - 1} + \dots + a_{k} x_{n - k}}{b_{0} x_{n} + b_{1} x_{n - 1} + \dots + b_{k} x_{n - k}}$

On boundedness of solutions of the difference equation $x_{n + 1} = (p x_{n} + q x_{n - 1}) / (1 + x_{n})$ for $q > 1 + p > 1$ .