On the recursive sequence xn+1=(α−βxn−k

Abstract

a b s t r a c tThis paper is devoted to investigating the asymptotic behavior of the recursive sequencewhere α ≥ 0 and β > 0 and g is continuous on R k . We show that under certain conditions this equation has a unique positive (negative) equilibrium point which is a global attractor with some basin S ⊂ R k+1 . Also we establish the oscillation of all solutions with initialWe apply these results to the recursive sequencewhere α, γ , a i , b i ≥ 0, i = 0, . . . , k − 1, and β > 0.