On the recursive sequence yn+1=α+yn-1β+yn+yn-1yn

We study the global stability, the boundedness character and the periodic nature of the positive solutions of the difference equationyn+1=α+yn-1β+yn+yn-1yn,n=0,1,2,…,where α, β ∈ (0, ∞), α ≠ β, β ≠ 2 and the initial conditions y−1, y0 are arbitrary positive real numbers.