The strong asymptotic equivalence and the generalized inverse

摘要

We discuss the relationship between the strong asymptotic equivalence relation and the generalized inverse in the class of all nondecreasing and unbounded functions, defined and positive on a half-axis [a, +∞) (a > 0). In the main theorem, we prove a proper characterization of the function class IRV∩, where IRV is the class of all -regularly varying functions (in the sense of Karamata) having continuous index function.