Good decomposition in the class of convex functions of higher order

The problems investigated in this article are connected to the fact that the class of slowly varying functions is not closed with respect to the operation of subtraction. We study the class of functions Fk?1, which are nonnegative and i-convex for 0<_ i < k, where k is a positive integer. We present necessary and sufficient condition that guarantee that, no matter how we decompose an additively slowly varying function L ? Fk?1 into a sum L = F + G, F,G ? Fk?1, then necessarily F and G are additively slowly varying.