Global attractivity of the difference equation xn+1=(xn+αxn-1)/(β+xn)

Our aim in this paper is to investigate the global attractivity of nonnegative solution of the difference equationxn+1=(xn+αxn-1)/(β+xn),n=0,1,…,where α > 0, β ⩾ 0 are real numbers, the initial conditions x−1, x0 are nonnegative real numbers and with β and x−1 not both zero. We show that the positive equilibrium point of the equation is a global attractor.