Abstract
The main objective of this paper was to study the global stability of the positive solutions and the periodic character of the difference equation
x(n+1) = ax(n-l) + bx(n-k) + cx(n-s)/dx(n-s)- e, n=0, 1, ...,
where the parameters a, b, c, d, and e are positive real numbers and the initial conditions x(-t), x(-t+1),...,x(-1), x(0) are positive real numbers where t = max{l, k, s}. Some numerical examples will be given to explicate our results. Copyright (C) 2016 JohnWiley & Sons, Ltd.