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Good decomposition in the class of convex functions of higher order. (English) Zbl 1246.26003
Summary: 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 $$\mathcal F_{k-1}$$, which are nonnegative and $$i$$-convex for $$0\leq i < k$$, 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 $$L\in\mathcal F_{k-1}$$ into a sum $$L = F+G$$, $$F,G\in\mathcal F_{k-1}$$, then necessarily $$F$$ and $$G$$ are additively slowly varying.
##### MSC:
 26A12 Rate of growth of functions, orders of infinity, slowly varying functions 26A51 Convexity of real functions in one variable, generalizations
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