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On Korenblum convex functions

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Lopez L. M., Ereú J., Merentes N.

Commentationes Mathematicae

2017

tom 57

nr 1

We introduce a new class of generalized convex functions called the \(\kappa\)-convex functions, based on Korenblum's concept of \(\kappa\)-decreasing functions, where \(\kappa\) 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 \(\kappa\)-variation, extending a result of F. Riesz. We also present a formal structural decomposition result for the \(\kappa\)-convex functions.

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1 Commentationes Mathematicae

1 Ereú J.

1 Lopez L. M.

1 Merentes N.

1 2017

Wyniki wyszukiwania

On Korenblum convex functions