An inequality for quasi-convex functions

Abstract

In this paper we prove that a real quasi-convex function ƒ satisfies, for any measurable set S symmetric with respect the point x⁰ the inequality:

where mis S denotes the measure of S. Also we prove that the inequality (1) characterizes a quasi- convex function if S belongs to a suitable family of symmetric sets.

Keywords:

• AMS (MOS) CLASSIFICATION 26-Functions of real variables