Global asymptotic stability in some discrete dynamical systems

For a discrete dynamical system x(n+1) = Tx(n) on M subset of R-r some gene ral conditions will be specified under which the unique equilibrium is glob ally asymptotically stable. As a special result we obtain the strong negati ve feedback property established ill A. M. Amleh, N. Kruse, and G. Ladas (J . Differ. Equations Appl. to appear). Finally we apply our result to show t hat the equilibrium x* = 1 of the Putnam difference equation, x(n+1) = x(n) + x(n-1) + x(n-2)x(n-3)/x(n)x(n-1) + x(n-2) + x(n-3), with positive initial conditions xo,...,x(-3), is globally asymptotically s table. (C) 1999 Academic Press.