Authors’ abstract: We study the global attractivity, the invariant intervals, the periodic and oscillatory character of the difference equation
where are positive real numbers, is a positive integer, and the initial conditions are nonnegative real numbers such that or or both are positive real numbers. We show that the positive equilibrium of the difference equation is a global attractor. As a corollary, our main result confirms a conjecture proposed by Kulenovic et al. (2003) [M. R. S. Kulenovic, G. Ladas, L. F. Martins, and I. W. Rodrigues, Comput. Math. Appl. 45, No. 6–9, 1087–1099 (2003; Zbl 1077.39004)].