Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

ON POSITIVE SOLUTIONS OF A RECIPROCAL DIFFERENCE EQUATION WITH MINIMUM

  • QINAR CENGIZ (Mathematics Department, Faculty of Education, Selcuk University) ;
  • STEVIC STEVO (Mathematical Institutte of Serbian Academy of Science) ;
  • YALQINKAYA IBRAHIM (Mathematics Department, Faculty of Education, Selcuk University)
  • Published : 2005.01.01

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Abstract

In this paper we consider positive solutions of the following difference equation $$x_{n+l}\;=\;min[{\frac{A}{x_{n}},{\frac{B}{x_{n-2}}}],\;A,B\;>\;0$$. We prove that every positive solution is eventually periodic. Also, we present here some results concerning positive solutions of the difference equation $$x_{n+l}\;=\;min[{\frac{A}{x_{n}x_{n-1}{\cdots}x_{n-k}},{\frac{B}{x_{n-(k+2)}{\cdots}x_{n-(2k+2)}}],\;A,B\;>\;0$$.

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