CONVERGENCE CRITERIA FOR A CLASS OF SECOND-ORDER DIFFERENCE EQUATIONS

This paper studies a class of nonlinear second order difference equations of the type x_n+1 = f(x_n, x_n−1) / x_n , where f is symmetric and monotonic with initial conditions x−1, x0 being positive real numbers. Some sufficient conditions under which every positive solution of such equation converges to a period two solution or to the cycle {0, ∞} are established.