Some results about the global attractivity of bounded solutions of difference equations with applications to periodic solutions

We obtain some results about the global attractivity of bounded solutions of difference equation where f is non-increasing or non-decreasing in each argument and every point in I is an equilibrium point of above equation where I is an invariant interval for this equation. By our results we prove that when k is an odd positive integer and p 1 is a real number, every positive solution of converges to a period-two solution of this equation. We also apply our results to the rational difference equation where k,l {0, 1, …}, and we show that every positive solution of this equation converges to a period-two solution of this equation.