ON EQUIVALENT SLOWLY VARYING FUNCTIONS - Danielian, I. E. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2001)
Let 0<t_0<t_1<...,_n→ +∞t_n=+∞, _n(t_n+1-t-n)<+∞. 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.