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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization of $B$-slowly varying functions
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by Steven Bloom PDF
Proc. Amer. Math. Soc. 54 (1976), 243-250 Request permission

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.
References
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 54 (1976), 243-250
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0393375-X
  • MathSciNet review: 0393375