On positive solutions of a reciprocal difference equation with minimum |
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Authors: | Cengiz Çinar Stevo Stević Ibrahim Yalçinkaya |
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Affiliation: | 1. Mathematics Department, Faculty of Education, Selcuk University, 42090, Konya, Turkey 2. Mathematical Institute of Serbian Academy of Science, Knez Mihailova 35/I, 11000, Beograd
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Abstract: | In this paper we consider positive solutions of the following difference equation $$x_{n + 1} = min left{ {frac{A}{{x_n }},frac{B}{{x_{n - 2} }}} right}, A, B > 0.$$ We prove that every positive solution is eventually periodic. Also, we present here some results concerning positive solutions of the difference equation $$x_{n + 1} = min left{ {frac{A}{{x_n x_{n - 1} ...x_{n - k} }},frac{B}{{x_{n - (k + 2)} ...x_{n - (2k + 2)} }}} right}, A, B > 0.$$ |
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