Opuscula Mathematica (Jan 2010)

On the global attractivity and the periodic character of a recursive sequence

  • E. M. Elsayed

DOI
https://doi.org/10.7494/OpMath.2010.30.4.431
Journal volume & issue
Vol. 30, no. 4
pp. 431 – 446

Abstract

Read online

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