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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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 generalization of slowly varying functions
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by D. Drasin and E. Seneta PDF
Proc. Amer. Math. Soc. 96 (1986), 470-472 Request permission

Abstract:

This note establishes that if the main part of the definition of a slowly varying function is relaxed to the requirement that lim ${\sup _{x \to \infty }}\psi (\lambda x)/\psi (x) < \beta < \infty$ for each $\lambda > 0$, then $\psi (x) = L(x)\theta (x)$, where $L$ is slowly varying and $\theta$ is bounded. This is done by obtaining a representation for the function $\psi$.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 96 (1986), 470-472
  • MSC: Primary 26A12
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0822442-5
  • MathSciNet review: 822442