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Global attractivity in a class of difference equations. (Chinese. English summary) Zbl 0982.39009

The author considers the difference equation \[ x_{n+1}= \frac{\alpha x_n}{(1+ \beta x_{n-k})^\lambda}, \quad n= 0,1,2,\dots, \] where \(\alpha\in (1,\infty)\), \(\beta,\lambda\in (0,\infty)\), and \(k\in \{1,2,3,\dots\}\). Several sufficient conditions are obtained which guarantee that the positive equilibrium is a global attractor.

MSC:

39B05 General theory of functional equations and inequalities
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