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Global attractivity of the recursive sequence\(x_{n + 1} = \frac{{\alpha - \beta x_{n - k} }}{{\gamma + x_n }}\)

  • H. M. El-Owaidy
  • A. M. Ahmed
  • Z. Elsady
Article

Abstract

Our aim in this paper is to investigate the global attractivity of the recursive sequence
$$x_{n + 1} = \frac{{\alpha - \beta x_{n - k} }}{{\gamma + x_n }},$$
where α, β, γ >0 andk=1,2,… We show that the positive equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients.

AMS Mathematics Subject Classification

39A10 39A99 34C99 

Key words and phrases

Difference equations higher order attractivity asymptotic stability 

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Copyright information

© Korean Society for Computational and Applied Mathematics 2004

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceAl-Azhar UniversityNasr City, CairoEgypt

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