Global Asymptotic Stability in Some Discrete Dynamical Systems

For a discrete dynamical system xnq1sTxn on M;Rr some general conditions will be specified under which the unique equilibrium is globally asymptotically stable. As a special result we obtain the strong negative feedback property established in A. M. Amleh, N. Kruse, and G. Ladas J. Differ. Equations Appl. to appear.. Finally we apply our result to show that the equilibrium x*s1 of the Putnam difference equation, xnqxny1qxny2xny3 xnq1s xnxny1qxny2qxny3 , with positive initial conditions x0, . . . , xy3 is globally asymptotically stable.