On the Difference equation xn+1 = Axn + B kΣi=0 xn-i/C+B kπi=0xn-i.

The main objective of this paper is to study the global stability of the positive solutions and the periodic character of the difference equation xn+1 = A kΣi=0 xn-i/B+C kπi=0xn-i, n=0, 1, ..., where the parameters A, B and C are positive real numbers and the initial conditions x-k, x-k+1, ..., x-, x0 are nonnegative real numbers. [ABSTRACT FROM AUTHOR]