Global attractivity for a family of nonlinear difference equations

In this note, we consider the following nonlinear difference equation: xn+1=f(xn−r1,…,xn−rk)g(xn−m1,…,xn−ml)+h(xn−p1,…,xn−ps)+1f(xn−r1,…,xn−rk)+g(xn−m1,…,xn−ml)+h(xn−p1,…,xn−ps),n=0,1,…, where f∈C((0,+∞)k,(0,+∞))f∈C((0,+∞)k,(0,+∞)), g∈C((0,+∞)l,(0,+∞))g∈C((0,+∞)l,(0,+∞)) and h∈C((0,+∞)s,[0,+∞))h∈C((0,+∞)s,[0,+∞)) with k,l,s∈{1,2,…}k,l,s∈{1,2,…}, 0≤r1<⋯