• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.375-382
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• 2007

We Study, firstly, the dynamics of the difference equation $x_{n+1}\;=\;{\alpha}\;+\;{\frac{x^p_n}{x^p_{n-1}}}$, with $p\;{\in}\;(0,\;1)\;and\;{\alpha}\;{\in}\;[0,\;{\infty})$. Then, we generalize our results to the (k + 1)th order difference equation $x_{n+1}\;=\;{\alpha}\;+\;{\frac{x^p_n}{nx^p_{n-k}}$, $k\;=\;2,\;3,\;{\cdots}$ with positive initial conditions.