Global stability for nonlinear difference equations with variable coefficients

Consider the following nonlinear difference equation with variable coefficients:{x(n+1)=x(n)−∑j=0maj(n)fj(x(n−j)),n=0,1,2,…,x(j)=xj,−m⩽j⩽0, where aj(n)⩾0aj(n)⩾0, 0⩽j⩽m0⩽j⩽m, ∑j=0maj(n)>0 and ∑n=0∞∑j=0maj(n)=+∞. We assume that there exists a strictly monotone increasing function f(x)f(x) on (−∞,+∞)(−∞,+∞) such that f(0)=0f(0)=0, 0