Strong Asymptotic Equivalence and Inversion of Functions in the Class Kc

In this paper we consider the class of functions Kc introduced by W. Matuszewska (1964, Studia Math. 24, 271–279) and W. Matuszewska and W. Orlicz (1965, Studia Math. 26, 11–24). As a main result we describe, in terms of the class Kc , when two strictly increasing functions, as well as their inverse functions, are asymptoticaly equivalent in the strong sense. This result also gives a proper characterization of the class Kc .