BY-NC-NDĐurčić, DraganNikolić, RaleTorgašev A.2021-12-052021-12-0520110363-1672https://scidar.kg.ac.rs/handle/123456789/13783We discuss the relationship between the weak and strong asymptotic equivalence relations and the generalized inverse in the class A of all nondecreasing unbounded positive functions on a half-axis [a,+∞) (a > 0). As a main result, we prove a proper characterization of the functional class R ∞ ∩ A, where R ∞ is the class of all rapidly varying functions. Also, we prove a characterization of the functional class PI * ∩ A.enopenAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/article10.1007/s10986-011-9141-5