Opuscula Math. 30, no. 4 (2010), 431-446
http://dx.doi.org/10.7494/OpMath.2010.30.4.431
Opuscula Mathematica
On the global attractivity and the periodic character of a recursive sequence
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.
Mathematics Subject Classification: 39A10.
- E. M. Elsayed
- Mansoura University, Faculty of Science, Mathematics Department, Mansoura 35516, Egypt
- King Abdulaziz University, Faculty of Science, Mathematics Department, Jeddah, Saudi Arabia
- Received: 2009-12-23.
- Revised: 2010-03-28.
- Accepted: 2010-04-06.
