2005 / June Volume 32 No.2
On the recursive sequence $x_{n+1}=\frac{\alpha_{1} x_n+\cdots+\alpha_{k} x_{n-k+1}}{A+f(x_n,\cdots,x_{n-k+1})}$
| Published Date |
2005 / June
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|---|---|
| Title | On the recursive sequence $x_{n+1}=\frac{\alpha_{1} x_n+\cdots+\alpha_{k} x_{n-k+1}}{A+f(x_n,\cdots,x_{n-k+1})}$ |
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| Pagination | 173-183 |
| Abstract | We investigate the behavior of solutions of the difference equation $x_{n+1}=\frac{ \alpha_1 x_n+\cdots+ \alpha_k x_{n-k+1}}{A+f(x_n,..., x_{n-k+1})}$, $n \ge k-1, k \in N$,
where the parameters $\alpha_i, i = 1, \ldots , k$, and initial conditions
${x_0, x_1, \ldots , x_{k?1}}$ are nonegative real numbers, $A > 0$ and where
the function f satisfies certain additional conditions. The main result in this note solves and generelizes an open problem in [11]. In the proof of the main result we do not use smoothness of the function $f$.
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| AMS Subject Classification |
not available
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| Received |
2003-12-30
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