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On the recursive sequence\(x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}\)

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Abstract

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the positive solutions of the difference equation of the form

$$x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}, n = 0,1,...$$

is investigated, where all the coefficients are nonnegative real numbers.

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Authors and Affiliations

  1. Mathematical Institute of Serbian Academy of Science, Knez Mihailova 35/I, 11000, Beograd

    Stevo Stević

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  1. Stevo Stević
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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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Stević, S. On the recursive sequence\(x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}\) . JAMC 18, 229–234 (2005). https://doi.org/10.1007/BF02936567

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  • DOI: https://doi.org/10.1007/BF02936567

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