Summary: This paper is concerned with the following nonlinear difference equation
where the initial data , , , are nonnegative integers, and and are arbitrary positive real numbers. We give sufficient conditions under which the unique equilibrium of this equation is globally asymptotically stable, which extends and includes corresponding results obtained in the work of C. Çinar [Appl. Math. Comput. 150, No. 1, 21–24 (2004; Zbl 1050.39005)], X. Yang et al. [Appl. Math. Comput. 162, No. 3, 1485–1497 (2005; Zbl 1068.39031)], and K. S. Berenhaut et al. [Appl. Math. Lett. 20, No. 1, 54–58 (2007; Zbl 1131.39006)]. In addition, some numerical simulations are also shown to support our analytic results.