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June 2020 New results on slowly varying functions in the Zygmund sense
Edward Omey, Meitner Cadena
Proc. Japan Acad. Ser. A Math. Sci. 96(6): 45-49 (June 2020). DOI: 10.3792/pjaa.96.009

Abstract

Very recently Seneta [15] has provided a characterization of slowly varying functions $L$ in the Zygmund sense by using the condition, for each $y>0$, \begin{equation} x\left(\frac{L(x+y)}{L(x)}-1\right)\to0 \text{ as } x\to∞. \tag{1} \end{equation} We extend this result by considering a wider class of functions and a more general condition than (1). Further, a representation theorem for this wider class is provided.

Citation

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Edward Omey. Meitner Cadena. "New results on slowly varying functions in the Zygmund sense." Proc. Japan Acad. Ser. A Math. Sci. 96 (6) 45 - 49, June 2020. https://doi.org/10.3792/pjaa.96.009

Information

Published: June 2020
First available in Project Euclid: 28 May 2020

MathSciNet: MR4103764
zbMATH: 07213227
Digital Object Identifier: 10.3792/pjaa.96.009

Subjects:
Primary: 26A12, 28A10, 45M05, 60G70

Rights: Copyright © 2020 The Japan Academy

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Vol.96 • No. 6 • June 2020
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