an:05595940
Zbl 1199.39025
Zayed, E. M. E.; El-Moneam, M. A.
On the rational recursive sequence \(x_{n+1}=\Big ( A+\sum _{i=0}^{k}\alpha _{i}x_{n-i}\Big ) \Big / \sum _{i=0}^{k}\beta _{i}x_{n-i}\)
EN
Math. Bohem. 133, No. 3, 225-239 (2008).
00252598
2008
j
39A22 39A20 39A30 39A23
boundedness character; period two solution; convergence; global stability; rational difference equation; positive solutions
Summary: 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
\[
x_{n+1}=\bigg ( A+\sum _{i=0}^{k}\alpha _{i}x_{n-i}\bigg ) \Big / \sum _{i=0}^{k}\beta _{i}x_{n-i},\;\;n=0,1,2,\dots
\]
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.