Global asymptotic stability of a family of difference equations

In this paper, we study the difference equation {xn=[f1f2f3+f1+f2+f3+hf1f2+f1f3+f2f3+g+h](xn−1,…,xn−r),n=1,2,…x1−r,x2−r,…,x0>0, where f1,f2,f3,g:(R+)r→R+f1,f2,f3,g:(R+)r→R+ and h:(R+)r→[0,+∞)h:(R+)r→[0,+∞) are all continuous functions. We present a sufficient condition for this difference equation to have a globally asymptotically stable equilibrium c=1c=1. This condition generalizes some previous results.