On the recursive sequence xn+1=(α−βxn−k)/g(xn,xn−1,…,xn−k+1)xn+1=(α−βxn−k)/g(xn,xn−1,…,xn−k+1)

This paper is devoted to investigating the asymptotic behavior of the recursive sequence xn+1=α−βxn−kg(xn,xn−1,…,xn−k+1),n=0,1,… where α≥0α≥0 and β>0β>0 and gg is continuous on RkRk. We show that under certain conditions this equation has a unique positive (negative) equilibrium point which is a global attractor with some basin S⊂Rk+1S⊂Rk+1. Also we establish the oscillation of all solutions with initial conditions {x−i}i=0k such that (x0,x−1,…,x−k)∈S(x0,x−1,…,x−k)∈S. We apply these results to the recursive sequence xn+1=α−βxn−kγ+∑k−1i=0(aixn−i±bixn−i2),n=0,1,… where α,γ,ai,bi≥0,i=0,…,k−1α,γ,ai,bi≥0,i=0,…,k−1, and β>0β>0.