Stability of solutions for the recursive sequence

In this paper, we investigate the global behavior of the recursive sequence x n + 1 = α - β x n γ + g ( x n - k ) for n = 0 , 1 , … , where α , β , γ ⩾ 0 and g ( x ) is a continuous function defined on ( - ∞ , ∞ ) , which satisfies some additional conditions.