| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2010-07-20T17:26:29Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140612 |
| . |
| Reference:
|
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| Reference:
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