Geodesic
On equivalent slowly varying functions
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2001), pp. 3-8

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Let $0$ For an upward convex slowly varying function $L(t)>0$ an equivalent slowly varying function $L_1(t)$ has been constructed that is convex, infinitely differentiable, and that coincides with $L(t)>0$ on a beforehand given numerical sequence $\{t_n\}$.
Keywords: slowly varying function. 
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I. E. Danielyan. On equivalent slowly varying functions. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2001), pp. 3-8. http://geodesic.mathdoc.fr/item/UZERU_2001_2_a0/