Some Notes on the Difference Equation xn+1=α+(xn−1/xnk)

We investigate the behavior of the solutions of the recursive sequence  xn+1=α+xn-1/xnk,  n=0,1,…, where α∈[0,∞), k∈(0,∞), and the initial conditions x-1,x0 are arbitrary positive numbers. Included are results that considerably improve those in the recently published paper by Hamza and Morsy (2009)