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

Abstract EN

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).