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On positive solutions of a reciprocal difference equation with minimum

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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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Correspondence to Stevo Stević.

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Stevo Stević received his Ph.D at Belgrade University in 2001. He has written more than 80 original scientific papers and his research interests are mostly in analytic functions of one and several variables, potential theory, difference equations, convergence and divergence of infinite limiting, nonlinear analysis, fixed point theory, operators on function spaces, inequalities and qualitative analysis of differential equations.

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Çinar, C., Stević, S. & Yalçinkaya, I. On positive solutions of a reciprocal difference equation with minimum. JAMC 17, 307–314 (2005). https://doi.org/10.1007/BF02936057

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  • DOI: https://doi.org/10.1007/BF02936057

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