On Korenblum convex functions

Lorena Maria Lopez, Jurancy Ereú, and Nelson Merentes. "On Korenblum convex functions." Commentationes Mathematicae 57.1 (2017): null. <http://eudml.org/doc/292499>.

@article{LorenaMariaLopez2017,
abstract = {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.},
author = {Lorena Maria Lopez, Jurancy Ereú, Nelson Merentes},
journal = {Commentationes Mathematicae},
keywords = {Convex function; $\kappa $-entropy; generalized convexity},
language = {eng},
number = {1},
pages = {null},
title = {On Korenblum convex functions},
url = {http://eudml.org/doc/292499},
volume = {57},
year = {2017},
}

TY - JOUR
AU - Lorena Maria Lopez
AU - Jurancy Ereú
AU - Nelson Merentes
TI - On Korenblum convex functions
JO - Commentationes Mathematicae
PY - 2017
VL - 57
IS - 1
SP - null
AB - 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.
LA - eng
KW - Convex function; $\kappa $-entropy; generalized convexity
UR - http://eudml.org/doc/292499
ER -