Global asymptotic stability in a delay difference equation (Q2779146)

The authors consider the nonlinear delay difference equation NEWLINE\[NEWLINE x_{n+1}-x_n+p_nx_{n-k}=f(n,x_{n-l}), \quad n=1,2,\dots, \tag \(*\) NEWLINE\]NEWLINE where \(p_n>0\), \(k,l\in \{0,1,2,\dots,\}\) and \(f(n,x)\) is continuous in \(x\in (-\infty,\infty)\) for each fixed \(n\). They obtain a sufficient condition for the global asymptotic stability of the zero solution of (\(*\)) which improves known results.