Global asymptotic stability in a class of generalized Putnam equations (Q2506413)

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 \(n=0,1,2,\dots\).