Attractivity of the recursive sequence xn+1=(α−βxn)F(xn−1,…,xn−k)xn+1=(α−βxn)F(xn−1,…,xn−k)

In this paper we investigate the global attractivity of the recursive sequence xn+1=(α−βxn)F(xn−1,…,xn−k),n=0,1,… where α,β≥0α,β≥0. We show that the unique positive equilibrium point of the equation is a global attractor with some basin. We apply this result to the rational recursive sequence xn+1=α−βxnγ+∑i=1kaixn−i+∑i=1kbixn−i2,n=0,1,… where α,β,ai,bi≥0α,β,ai,bi≥0 and γ>0γ>0, and prove that the positive equilibrium point of the equation is a global attractor with a basin that depends on certain conditions posed on the coefficients.