On the global behavior of higher order recursive sequences

Our basic purpose in this paper is to establish some conditions for the global attractivity and convergence of the kth-order recursive sequencexn=f(xn-1,xn-2,…,xn-k),n=1,2,3,…We will show that if f is a real-valued function with a convex basin Ω in Rk, which is differentiable with bounded differential, then f has an equilibrium point. Our final comments are about informative examples.