Revisiting extensions of regularly varying functions

Abstract

Relationships among the classes $\mathcal{M}$, ${\mathcal{M}}_{\infty }$, and ${\mathcal{M}}_{-\infty }$ and the class of \emph{O}-regularly varying functions are shown. These results are based on two characterizations of $\mathcal{M}$, ${\mathcal{M}}_{\infty }$, and ${\mathcal{M}}_{-\infty }$ provided by Cadena and Kratz in [7] and a new one given in this note.