Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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GLOBAL ATTRACTIVITY OF THE RECURSIVE SEQUENCE $x_{n+1}\;=\;\frac{{\alpha}\;-\;{\beta}x_{n-\kappa}}{{\gamma}+x_n}$

  • El-Owaidy, H.M. (Mathematics Department, Faculty of Science, Al-Azhar University) ;
  • Ahmed, A.M. (Mathematics Department, Faculty of Science, Al-Azhar University) ;
  • Elsady, Z. (Mathematics Department, Faculty of Science, Al-Azhar University)
  • 발행 : 2004.09.01

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초록

Our aim in this paper is to investigate the global attractivity of the recursive sequence $x_{n+1}\;=\;\frac{{\alpha}\;-\;{\beta}x_{n-\kappa}}{{\gamma}+x_n}$, where ${\alpha},\;{\beta},\;{\gamma}\;>\;0\;and\;{kappa}\;=\;1,\;2,\;{\ldots}$ 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.

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