On Korenblum convex functions

• Autorzy: Lorena Maria Lopez , Jurancy Ereú , Nelson Merentes
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Convex function; \(\kappa\)-entropy; generalized convexity

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2017
• Tom: 57
• Numer: 1

Daty

wydano

2017

online

2017-09-18

Twórcy

autor

Lorena Maria Lopez

autor

Jurancy Ereú

autor

Nelson Merentes

Identyfikatory

DOI

10.14708/cm.v57i1.1542