Global attractivity in Wazewska-Lasota difference model (Q1374833)

Using the method of diminishing intervals the author obtains a sufficient condition for the global attractivity of the positive equilibrium point of the delay difference equation \[ N_{n+1}- N_n= -\delta N_n+ Pe^{-a N_{n-k}},\quad n=0,1,\dots, \] where \(k\) is a nonnegative integer and \(a\), \(P\) and \(\delta\) are real numbers such that \(a>0\), \(P>\delta\), \(1>\delta>0\).