Stability of solutions for the recursive sequence xn+1=(α-βxn)/(γ+g(xn-k))

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