Global asymptotic stability of a nonlinear second-order difference equation (Q1886954)

A global stability result for a second order difference equation \(x_{n+1}=f(x_n, x_{n-1})\), \(n=0,1,\dots\), is proved assuming that \(f\) is decreasing in each of its arguments. It should be noticed that the main result of the paper can be derived from a more general result for a difference equation of arbitrary order \(k\geq 1\) established by \textit{H. A. El-Morshedy} [Comput. Math. Appl. 45, No. 4--5, 749--758 (2003; Zbl 1036.39008)].