Global behavior of a higher order difference equation

In this paper we study the global behavior of the nonnegative equilibrium points of the difference equation xn+1=Axn−mB+C∏i=02k+1xn−i,n=0,1,… where A,B,CA,B,C are nonnegative parameters, initial conditions are nonnegative real numbers and k,mk,m are nonnegative integers, m≤2k+1m≤2k+1. Also we derive solutions of some special cases of this equation.