# On ω-convex functions

Banach Center Publications (2011)

- Volume: 92, Issue: 1, page 351-359
- ISSN: 0137-6934

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topTomasz 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 -

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