Asymptotic similarity relation and generalized inverse

Abstract

In this paperwediscuss relationshipsamongasymptotic similarity, weak asymptotic equivalence and the generalized inverse in the class A of all nondecreasing unbounded positive functions on a halfaxis [a,+∞) (a > 0). As a main result, we prove proper characterizations of some classes of functions in Karamata's theory of regular and rapid variation.