The author proves that the equilibrium solution is globally asymptotically stable for the difference equations
where the initial values are positive, the parameter is nonnegative, but different from each other, and . In his proof he utilizes a global convergence result due to N. Kruse and T. Nesemann [J. Math. Anal. Appl. 235, 151–158 (1999; Zbl 0933.37016)]. In addition, using an inclusion theorem due to L. Berg [J. Difference Equ. Appl. 10, 399–408 (2004; Zbl 1056.39003)], he finds asymptotics of some solutions of the above difference equations.