ON EQUIVALENT SLOWLY VARYING FUNCTIONS

Abstract

Let $0<t_0<t_1<...,\lim\limits_{n\rightarrow +\infty}t_n=+\infty, \sup\limits_{n}(t_{n+1}-t-n)<+\infty.$ 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 ${t_n}$.