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On second κ -variation

Jurancy Josefina Ereú;  Lorena Maria Lopez;  Nelson José Merentes — 2016

Commentationes Mathematicae

We present the notion of bounded second κ -variation for real functions defined on an interval [ a , b ] . We introduce the class κ B V 2 ( [ a , b ] ) of all functions of bounded second κ -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.

On Korenblum convex functions

Lorena Maria Lopez;  Jurancy Ereú;  Nelson Merentes — 2017

Commentationes Mathematicae

We introduce a new class of generalized convex functions called the κ -convex functions, based on Korenblum’s concept of κ -decreasing functions, where κ 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 κ -variation, extending a result of F. Riesz. We also present...

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