On the recursive sequence \(x_{n+1}=\alpha+\frac{x^p_{n-1}}{x_n^p}\). (English) Zbl 1078.39013

Stević, Stevo

J. Appl. Math. Comput. 18, No. 1-2, 229-234 (2005).

The asymptotic behaviour of the solutions of the difference equation in the title is investigated for positive \(p\) and nonnegative \(\alpha\). Moreover, a convergence theorem is proved concerning the equation \(x_{n+1}=\alpha+f(x_{n-k}/x_n)\).

Reviewer: Lothar Berg (Rostock)

MSC:

39A11	Stability of difference equations (MSC2000)
39A20	Multiplicative and other generalized difference equations

Keywords:

asymptotic behaviour; rational difference equation; convergence

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