E. M. Elabbasy, H. El-Metwally, E. M. Elsayed, Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt, e-mail: emelabbasy@mans.edu.eg, helmetwally@mans.edu.eg, emelsayed@mans.edu.eg
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{a_0x_n+a_1x_{n-1}+\dots+a_kx_{n-k}}{b_0x_n+b_1x_{n-1}+\dots+b_kx_{n-k}}, n=0,1,\dots \^^M\end{equation*} where the parameters $ a_i$ and $b_i$ for $i=0,1,\dots,k$ are positive real numbers and the initial conditions $x_{-k},x_{-k+1},\dots,x_0$ are arbitrary positive numbers.
Keywords: stability, periodic solution, difference equation
Classification (MSC 2000): 39A10
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