Some discussions on the difference equation xn+1 = α + (xmn-1/xkn)

We give in this work the sufficient conditions on the positive solutions of the difference equation xn+1 = α + (xmn-1/xkn),n = 0,1,...,where α,k,and m ∈ (0,∞) under positive initial conditions x-1,x0 to be bounded,α-convergent,the equilibrium point to be globally asymptotically stable and that every positive solution converges to a prime two-periodic solution. our results coincide with that known for the cases m = k = 1 of amleh et al. (1999) and m = 1 of hamza and morsy (2009). we offer improving conditions in the case of m = 1 of gümüs and öcalan (2012) and explain our results by some numerical examples with figures. © 2015 awad a. bakery.