@Article{Elsayed2010,
author = "Elsayed, E. M.",
title = "On the global attractivity and the periodic character of a recursive sequence",
journal = "Opuscula Math.",
year = "2010",
volume = "30",
number = "4",
pages = "431--446",
doi = "http://dx.doi.org/10.7494/OpMath.2010.30.4.431",
url = "http://dx.doi.org/10.7494/OpMath.2010.30.4.431",
abstract = "In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence \[x_{n+1} = ax_n + \frac{bx_{n-1}+cx_{n+2}}{dx_{n-1}+ex_{n+2}}, \quad n=0,1,\ldots,\] where the parameters \(a\), \(b\), \(c\), \(d\) and \(e\) are positive real numbers and the initial conditions \(x_{-2}\), \(x_{-1}\), and \(x_0\) are positive real numbers.",
keywords = "stability, periodic solutions, boundedness, difference equations",
issn = "1232-9274"
}