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Logarithmically Convex Function

A function f(x) is logarithmically convex on the interval [a,b] if f>0 and lnf(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,infty) functions (Dharmadhikari and Joag-Dev 1988, p. 18).

See also

Convex Function, Logarithmically Concave Function

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References

Dharmadhikari, S. and Joag-Dev, K. Unimodality, Convexity, and Applications. Boston, MA: Academic Press, 1988.Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1100, 2000.

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Logarithmically Convex Function

Cite this as:

Weisstein, Eric W. "Logarithmically Convex Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LogarithmicallyConvexFunction.html

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