On the recursive sequence xn + 1 = α+βxn - 1/1 + g (xn)

Abstract

We investigate the boundedness character, the oscillatory and periodic nature, and the global stability behaviour of the nonnegative solutions of the difference equation xn + 1 = α+βxn - 1/1 + g (xn), where the parameters α and β are nonnegative real numbers and g(x) is a continuous function on [0, ∞), which satisfies some additional conditions.