On ω-convex functions

Tomasz Szostok. "On ω-convex functions." Banach Center Publications 92.1 (2011): 351-359. <http://eudml.org/doc/281772>.

@article{TomaszSzostok2011,
abstract = {In Orlicz spaces theory some strengthened version of the Jensen inequality is often used to obtain nice geometrical properties of the Orlicz space generated by the Orlicz function satisfying this inequality. Continuous functions satisfying the classical Jensen inequality are just convex which means that such functions may be described geometrically in the following way: a segment joining every pair of points of the graph lies above the graph of such a function. In the current paper we try to obtain a similar geometrical description of the aforementioned inequality.},
author = {Tomasz Szostok},
journal = {Banach Center Publications},
keywords = {Orlicz function; Beckenbach convexity; Jensen inequality; Orlicz space},
language = {eng},
number = {1},
pages = {351-359},
title = {On ω-convex functions},
url = {http://eudml.org/doc/281772},
volume = {92},
year = {2011},
}

TY - JOUR
AU - Tomasz Szostok
TI - On ω-convex functions
JO - Banach Center Publications
PY - 2011
VL - 92
IS - 1
SP - 351
EP - 359
AB - In Orlicz spaces theory some strengthened version of the Jensen inequality is often used to obtain nice geometrical properties of the Orlicz space generated by the Orlicz function satisfying this inequality. Continuous functions satisfying the classical Jensen inequality are just convex which means that such functions may be described geometrically in the following way: a segment joining every pair of points of the graph lies above the graph of such a function. In the current paper we try to obtain a similar geometrical description of the aforementioned inequality.
LA - eng
KW - Orlicz function; Beckenbach convexity; Jensen inequality; Orlicz space
UR - http://eudml.org/doc/281772
ER -