Edward Omey, Meitner Cadena
Proc. Japan Acad. Ser. A Math. Sci. 96 (6), 45-49, (June 2020) DOI: 10.3792/pjaa.96.009
KEYWORDS: slowly varying, monotony in the Zygmund sense, class $\Gamma_{a}(g)$, self-neglecting function, Extreme value theory, Convergence rates, 26A12, 28A10, 45M05, 60G70
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.
