PUBLICATIONS DE L'INSTITUT MATH\'EMATIQUE (BEOGRAD) (N.S.) EMIS ELibM Electronic Journals Publications de l'Institut Mathématique (Beograd)
Vol. 73(87), pp. 53-57 (2003)

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ON THE CLASSES OF RAPIDLY VARYING FUNCTIONS

Slavko Simi\'c

Matemati\v cki institut SANU, Kneza Mihaila 35, Beograd, Serbia

Abstract: The classes $KR_\infty$, $MR_\infty$, $R_\infty$ of rapidly varying functions are natural extensions of Karamata's concept of regular variation. In \cite{2} we introduced a new class $K$ of perfect Karamata's kernels and its subclasses $\Theta$ and $\Sigma$. In this paper we study inclusion properties of these classes and, among other results, we prove $KR_\infty\subset MR_\infty\subset\Sigma\subset\Theta\subset K$.

Classification (MSC2000): 26A12

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