On the rational difference equation y n +1 = A + y n / y n-k

Abstract

We find conditions for the global asymptotic stability of the unique negative equilibrium y- = 1 + A of the equation yn+1 = A + yn/yn-k, where y-k, y-k+1,...,y0, A ∈ R, and k ∈ {1,2,3,4,...}