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On Korenblum convex functions

100%

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.

On second \(\kappa\)-variation

100%

Ereú J. J., Lopez L. M., Merentes N. J.

Commentationes Mathematicae

2016

tom 56

nr 2

We present the notion of bounded second \(\kappa\)-variation for real functions defined on an interval \([a,b]\). We introduce the class \(\kappa BV^{2}([a,b])\) of all functions of bounded second \(\kappa\)-variation on \([a,b]\). We show several properties of this class and present a sufficient condition under which a composition operator acts between these spaces.

Ograniczanie wyników

2 Commentationes Mathematicae

2 Lopez L. M.

1 Ereú J.

1 Ereú J. J.

1 Merentes N.

1 Merentes N. J.

1 2017

1 2016

Wyniki wyszukiwania

On Korenblum convex functions

On second \(\kappa\)-variation