EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 80(94), pp. 157–169 (2006)

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GOOD DECOMPOSITION IN THE CLASS OF CONVEX FUNCTIONS OF HIGHER ORDER

Slobodanka Jankovic and Tatjana Ostrogorski

Matematicki institut SANU, Kneza Mihaila 35, Beograd, Serbia

Abstract: 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.

Classification (MSC2000): 26A12

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Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 4 Dec 2006.

© 2006 Mathematical Institute of the Serbian Academy of Science and Arts
© 2006 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition