Proceedings of the Japan Academy, Series A, Mathematical Sciences

New results on slowly varying functions in the Zygmund sense

Edward Omey and Meitner Cadena

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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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 96, Number 6 (2020), 45-49.

Dates
First available in Project Euclid: 28 May 2020

Permanent link to this document
https://projecteuclid.org/euclid.pja/1590652896

Digital Object Identifier
doi:10.3792/pjaa.96.009

Mathematical Reviews number (MathSciNet)
MR4103764

Zentralblatt MATH identifier
07213227

Subjects
Primary: 26A12: Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48] 28A10: Real- or complex-valued set functions 45M05: Asymptotics 60G70: Extreme value theory; extremal processes

Keywords
Slowly varying monotony in the Zygmund sense class $\Gamma_{a}(g)$ self-neglecting function extreme value theory convergence rates

Citation

Omey, Edward; Cadena, Meitner. New results on slowly varying functions in the Zygmund sense. Proc. Japan Acad. Ser. A Math. Sci. 96 (2020), no. 6, 45--49. doi:10.3792/pjaa.96.009. https://projecteuclid.org/euclid.pja/1590652896


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