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

Abstract

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the nonnegative solutions of the difference equation of the form (Equation presented) is investigated, where α > 0, k ∈ N and /: [0, ∞)k → (0, ∞) is a continuous function nondecreasing in each variable.