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Title: 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} $ (English)
Author: Zayed, E. M. E.
Author: El-Moneam, M. A.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 133
Issue: 3
Year: 2008
Pages: 225-239
Summary lang: English
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Category: math
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Summary: 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 $A$, $\alpha _i$, $\beta _i$ 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. (English)
Keyword: difference equations
Keyword: boundedness character
Keyword: period two solution
Keyword: convergence
Keyword: global stability
MSC: 34C99
MSC: 39A10
MSC: 39A11
MSC: 39A20
MSC: 39A22
MSC: 39A23
MSC: 39A30
MSC: 39A99
idZBL: Zbl 1199.39025
idMR: MR2494777
DOI: 10.21136/MB.2008.140612
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Date available: 2010-07-20T17:26:29Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/140612
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