Abstract
The main objective of this paper is to study the periodic character and the global stability of the positive solutions of the difference equation
Xn+1 = ax(n) + bx(n-k) + cx(n-l) - dx(n-s)/ex(n-s) - alpha x(n-t) , n = 0, 1, ... ,
where the parameters a, b, c, d, e and alpha are positive real numbers and the initial conditions x(-sigma), x(-sigma+1), ... , x(-1), x(0) are positive real numbers where sigma = max{s, t, l, k}. Some numerical examples were given to illustrate our results.