On the rational recursive sequence $ \ x_{n+1}=\Big ( A+\sum _{i=0}^k\alpha _ix_{n-i}\Big ) \Big / \sum _{i=0}^k\beta _ix_{n-i} $

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

doi:10.21136/MB.2008.140612

Geodesic

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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}

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

Mathematica Bohemica, Tome 133 (2008) no. 3, pp. 225-239.

Voir la notice de l'article dans Czech Digital Mathematics Library

Résumé

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 \[ x_{n+1}=\bigg ( A+\sum _{i=0}^k\alpha _ix_{n-i}\bigg ) \Big / \sum _{i=0}^k\beta _ix_{n-i},\ \ n=0,1,2,\dots \] 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.

MR Zbl

DOI : 10.21136/MB.2008.140612

Classification : 34C99, 39A10, 39A11, 39A20, 39A22, 39A23, 39A30, 39A99
Mots-clés : difference equations; boundedness character; period two solution; convergence; global stability

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Zayed, E. M. E.; El-Moneam, M. A. On the rational recursive sequence $ \ x_{n+1}=\Big ( A+\sum _{i=0}^k\alpha _ix_{n-i}\Big ) \Big / \sum _{i=0}^k\beta _ix_{n-i} $. Mathematica Bohemica, Tome 133 (2008) no. 3, pp. 225-239. doi : 10.21136/MB.2008.140612. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2008.140612/

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