THE GLOBAL ATTRACTIVITY OF THE RATIONAL DIFFERENCE EQUATION yn = A+ (yn-k/yn-m)p

This paper studies the behavior of positive solutions of the recursive equation yn= A + (y n-k /y n-m ) p , n = 0, 1, 2,..., with y-s, y-s+1,..., y-1 ∈ (0, ∞) and k,m ∈ {1,2,3,4,...}, where s = max{k,m}. We prove that if gcd(k,m) = 1, and p < min{1,(A +1)/2}, then y n tends to A + 1. This complements several results in the recent literature, including the main result in K. S. Berenhaut, J. D. Foley and S. Stevic, The global attractivity of the rational difference equation y n = 1 + y n-k /y n-k , Proc. Amer. Math. Soc., 135 (2007) 1133-1140.