On the Difference Equationxn+1=∑kj=0ajfj(xn−j)

Abstract

This paper studies the boundedness character and the global attractivity of positive solutions of the difference equation xn+1 = ∑j=0akjfj (xn-j), n ∈ N0, where aj are positive numbers and fj are continuous decreasing self-maps of the interval (0, ∞) for j = 0, 1,...,k.