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Convexity, logarithmic

From Encyclopedia of Mathematics
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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=39512
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article