On the recursive sequence xn+1 = α + βx n-k/f(xn, ..., xn-k+1)

Abstract

The boundedness, the oscillatory behavior and the global stability of the nonnegative solutions of the difference equation xn+1 = α + βxn-k/f(xn, ..., xn-k+1) is investigated, where k ∈ N, the parameters α and β are nonnegative real numbers and f : R+k → R+ is a continuous function nondecreasing in each variable such that f(0, ..., 0) > 0.