Abstract
In this paper we study the behavior of the difference equation
x(n+1) = alpha x(n)x(n-l)/beta x(n-m) + gamma x(n-l), n = 0,1, ...,
where the initial conditions x(-r), x(-r+1), ..., x(0) are arbitrary non zero real numbers where r = max{l,m} is a non-negative integer and alpha, beta and gamma are constants. Also, we obtain the solutions of some special cases of this equation. At the end we present some numerical examples to support our theoretical discussion.