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)+1f(xn−r1,…,xn−rk)+g(xn−m1,…,xn−ml),n=0,1,…, where f∈C(k(0,+∞),(0,+∞))f∈C((0,+∞)k,(0,+∞)) and g∈C(l(0,+∞),(0,+∞))g∈C((0,+∞)l,(0,+∞)) with k,l∈{1,2,…}k,l∈{1,2,…}, 0⩽r1<⋯