On the difference equation ${ x_{n+1}=\frac{ax_{n}^{2}+bx_{n-1}x_{n-k}}{cx_{n}^{2}+dx_{n-1}x_{n-k}}}
In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence \begin{equation*}x_{n+1}=\frac{ax_{n}^{2}+bx_{n-1}x_{n-k}}{cx_{n}^{2}+dx_{n-1}x_{n-k}},\;\;\;n=0,1,\dots\end{equation*}where the parameters $a,b,c$ and $d$ are positive rea...
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| Published in | Sarajevo journal of mathematics Vol. 4; no. 2; pp. 239 - 248 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
11.06.2024
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| Online Access | Get full text |
| ISSN | 1840-0655 2233-1964 |
| DOI | 10.5644/SJM.04.2.09 |
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| Abstract | In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence
\begin{equation*}x_{n+1}=\frac{ax_{n}^{2}+bx_{n-1}x_{n-k}}{cx_{n}^{2}+dx_{n-1}x_{n-k}},\;\;\;n=0,1,\dots\end{equation*}where the parameters $a,b,c$ and $d$ are positive real numbers and the initial conditions $ x_{-k},x_{-k+1},\dots,x_{-1}$ and $x_{0}$ are arbitrary positive numbers.
2000 Mathematics Subject Classification. 39A10 |
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| AbstractList | In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence
\begin{equation*}x_{n+1}=\frac{ax_{n}^{2}+bx_{n-1}x_{n-k}}{cx_{n}^{2}+dx_{n-1}x_{n-k}},\;\;\;n=0,1,\dots\end{equation*}where the parameters $a,b,c$ and $d$ are positive real numbers and the initial conditions $ x_{-k},x_{-k+1},\dots,x_{-1}$ and $x_{0}$ are arbitrary positive numbers.
2000 Mathematics Subject Classification. 39A10 |
| Author | Elsayed, E.M. Elabbasy, E. M. El-Metwally, H. |
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| Title | On the difference equation ${ x_{n+1}=\frac{ax_{n}^{2}+bx_{n-1}x_{n-k}}{cx_{n}^{2}+dx_{n-1}x_{n-k}}} |
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