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

E. M. Elsayed

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.

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