| Title:
|
On the rational recursive sequence $ x_{n+1}=\dfrac {\alpha_0x_n+\alpha_1x_{n-l}+\alpha _2x_{n-k}} {\beta_0x_n+\beta_1x_{n-l}+\beta_2x_{n-k}}$ (English) |
| Author:
|
Zayed, E. M. E. |
| Author:
|
El-Moneam, M. A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
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0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
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135 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
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319-336 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $$ x_{n+1}=\frac {\alpha _0x_n+\alpha _1x_{n-l}+\alpha _2x_{n-k}} {\beta _0x_n+\beta _1x_{n-l}+\beta _2x_{n-k}}, \quad n=0,1,2,\dots $$ where the coefficients $\alpha _i,\beta _i\in (0,\infty )$ 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. (English) |
| Keyword:
|
difference equation |
| Keyword:
|
boundedness |
| Keyword:
|
period two solution |
| Keyword:
|
convergence |
| Keyword:
|
global stability |
| MSC:
|
34C99 |
| MSC:
|
39A10 |
| MSC:
|
39A20 |
| MSC:
|
39A22 |
| MSC:
|
39A23 |
| MSC:
|
39A30 |
| MSC:
|
39A99 |
| MSC:
|
65Q10 |
| idZBL:
|
Zbl 1224.39015 |
| idMR:
|
MR2683642 |
| DOI:
|
10.21136/MB.2010.140707 |
| . |
| Date available:
|
2010-07-20T18:49:54Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140707 |
| . |
| Reference:
|
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