Asymptotic and boundedness behaviour of a rational difference equation

Abstract

In this work, we investigate the asymptotic behaviour and examine boundedness of the solutions for the following difference equation xn+1 = αλ−(nxn+(n−k)xn−k ) β + nxn + (n − k)xn−k , n = 0, 1, 2, ... (1) where λ ≥ 1 and α, β ≥ 0 and x−k, x−(k−1), ... , x−1, x0 are arbitrary numbers.