On the recursive sequence yn+1 = (alpha+yn-1)/(beta+yn) + yn-1/yn

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