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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A characterization of $ B$-slowly varying functions

Author: Steven Bloom
Journal: Proc. Amer. Math. Soc. 54 (1976), 243-250
MathSciNet review: 0393375
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Abstract: A measurable function $ \varphi > 0$ that satisfies the limit condition $ {\lim _{x \to \infty }}(\varphi (x + t\varphi (x))/\varphi (x)) = 1$ for all $ t$ is said to be $ B$-slowly varying. If $ \varphi $ is continuous, this limit is shown to hold uniformly for $ t$ in compact sets, and an integral representation is derived.

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PII: S 0002-9939(1976)0393375-X
Article copyright: © Copyright 1976 American Mathematical Society