Abstract
Our aim in this paper is to study the global stability character and the periodic nature of the solutions of the difference equation
x(n+1) = ax(n-l) + bx(n-k) + cx(n-s)/d + ex(n-t), n = 0,1, ...,
where the initial conditions x(-r), x(-r+1), x(-r+2), ..., x(0) are arbitrary positive real numbers, r = max{l, k, s, t} is nonnegative integer and a, b, c, d, e are positive constants.