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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-24,
author = {Tomasz Szostok},
title = {On $\omega$-convex functions},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {351-359},
zbl = {1255.39022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-24}
}
Tomasz Szostok. On ω-convex functions. Banach Center Publications, Tome 95 (2011) pp. 351-359. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-24/