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Global asymptotic stability in a class of generalized Putnam equations. (English) Zbl 1104.39012

The author proves that for every \(m\geq 3\) there is a unique equilibrium point that attracts globally all other solutions to the so-called “generalized Putnam equations” of the form \[ x_{n+1}= \left(\sum_{i=0}^{m-2} x_{n-i} + x_{n-m+1}x_{n-m})/(x_nx_{n-1} + \sum_{i=2}^mx_{n-i}\right), \] where \(n=0,1,2,\dots\).

MSC:

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

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