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
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
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