Convexity, logarithmic

From Encyclopedia of Mathematics
Revision as of 16:56, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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:,_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