The weak asymptotic equivalence and the generalized inverse

Abstract

In this paper, we discuss the relationship between the weak asymptotic equivalence relation and the generalized inverse in the class A{\mathcal{A}} 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 functional class ORV ÇA{{ORV} \cap \mathcal{A}} , where ORV is the class of all O{\mathcal{O}} -regularly varying functions (in the sense of Karamata). Keywordsregular variation-generalized inverse-weak asymptotic equivalence MSC26A12