Short Note: A Note on Periodic Character of a Difference Equation

In this note, we study positive solutions of the difference equation where and We prove that if then every positive solution converges to the positive equilibrium and if then every positive solution converges to a 2s-periodic solution. The second result generalizes the main result in the paper: W.T. Patula and H.D.Voulov, On the oscillation and periodic character of a third order rational difference equation, Proc. Amer. Math. Soc. 131 (3) (2003), 905–909.