Global asymptotic stability of a higher order rational difference equation

In this note, we consider the following rational difference equation: xn+1 = f (xn−r1, . . . , xn−rk )g(xn−m1, . . . , xn−ml ) +1 f (xn−r1, . . . , xn−rk ) +g(xn−m1, . . . , xn−ml ) , n= 0, 1, . . . , where f ∈ C((0,+∞)k, (0,+∞)) and g ∈ C((0,+∞)l, (0,+∞)) with k, l ∈ {1, 2, . . .}, 0 r1 < ··· < rk and 0 m1 < ···