On the rational difference equation yn+1=A+ynyn-k

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