## On $\omega$-convex functions

### Volume 92 / 2011

Banach Center Publications 92 (2011), 351-359
MSC: Primary 39B62; Secondary 26A51, 46E30.
DOI: 10.4064/bc92-0-24

#### 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.