The weak and the strong equivalence relation and the asymptotic inversion

Abstract

In this paper we discuss the relationship between the weak and the strong asymptotic equivalence relation and the asymptotic inversion, for positive and measurable functions defined on a half-axis [a, + ∞) (a > 0). As the main results, we prove a certain characterizations of the functional class of all rapidly varying functions, as well as some other functional classes.