Convex additively slowly varying functions |
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Authors: | Slobodanka Jankovi?Tatjana Ostrogorski |
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Institution: | Mathematical Institute, Kneza Mihaila 35, 11000 Belgrade, Yugoslavia |
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Abstract: | We study the problem of subtraction of slowly varying functions. It is well-known that the difference of two slowly varying functions need not be slowly varying and we look for some additional conditions which guarantee the slow variation of the difference. To this end we consider all possible decompositions L=F+G of a given increasing convex additively slowly varying function L into a sum of two increasing convex functions F and G. We characterize the class of functions L for which in every such decomposition the summands are necessarily additively slowly varying. The class OΠ2+ we obtain is related to the well-known class OΠg where, instead of first order differences as in OΠg, we have second order differences. |
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