## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### New results on slowly varying functions in the Zygmund sense

#### Abstract

Very recently Seneta [15] has provided a characterization of slowly varying functions $L$ in the Zygmund sense by using the condition, for each $y>0$, $$x\left(\frac{L(x+y)}{L(x)}-1\right)\to0 \text{ as } x\to∞. \tag{1}$$ 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

https://projecteuclid.org/euclid.pja/1590652896

Digital Object Identifier
doi:10.3792/pjaa.96.009

Mathematical Reviews number (MathSciNet)
MR4103764

Zentralblatt MATH identifier
07213227

#### 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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