logarithmically convex function

Input interpretation

logarithmically convex function

Alternate name

logconvex function

Definition

A function f(x) is logarithmically convex on the interval [a, b] if f>0 and ln f(x) is convex on [a, b]. If f(x) and g(x) are logarithmically convex on the interval [a, b], then the functions f(x) + g(x) and f(x) g(x) are also logarithmically convex on [a, b]. The definition can also be extended to R^k->(0, ∞) functions.
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Related terms

convex function | logarithmically concave function

Subject classifications

MathWorld

functions

MSC 2010

33-XX
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