Geodesic
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
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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.
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.
DOI : 10.21136/MB.2008.140612
Classification : 34C99, 39A10, 39A11, 39A20, 39A22, 39A23, 39A30, 39A99
Keywords: 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

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