On Korenblum convex functions

We introduce a new class of generalized convex functions called the K-convex functions, based on Korenblum’s concept of k-decreasing functions, where K is an entropy (distortion) function. We study continuity and differentiability properties of these functions, and we discuss a special subclass which is a counterpart of the class of so-called d.c. functions. We characterize this subclass in terms of the space of functions of bounded second k-variation, extending a result of F. Riesz. We also present a formal structural decomposition result for the K-convex functions.

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Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).