Global behavior of solutions of a nonlinear difference equation

Our aim in this paper is to investigate the persistence and the global attractivity of solutions of the equation x(n+1) = f(x(n), x(n-1), ..., x(n-k)) for n = 0,1, ..., where f is a continuous, positive and decreasing function on [(0, infinity)(k+1), (0, infinity)]. The results are applied to the difference equation y(n+1) = A/y(n)(p) +1/y(n-k)(q) for n = 0, 1, ..., where A, p, q is an element of (0, infinity), k is an element of {2, 3, ...}. (C) 2003 Elsevier Inc. All rights reserved.