# Convexity, logarithmic

From Encyclopedia of Mathematics

The property of a non-negative function , defined on some interval, that can be described as follows: If for any and in this interval and for any , with the inequality

is satisfied, is called logarithmically convex. If a function is logarithmically convex, it is either identically equal to zero or is strictly positive and is a convex function (of a real variable).

**How to Cite This Entry:**

Convexity, logarithmic.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Convexity,_logarithmic&oldid=11737

This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article