Opuscula Mathematica
Opuscula Math. 30, no. 4 (), 431-446
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.
Cite this article as:
E. M. Elsayed, On the global attractivity and the periodic character of a recursive sequence, Opuscula Math. 30, no. 4 (2010), 431-446, http://dx.doi.org/10.7494/OpMath.2010.30.4.431
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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