# logarithmically convex function

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## logarithmically convex function

[‚läg·ə¦rith·mik·lē ¦kän¦veks ‚fəŋk·shən]
(mathematics)
A function whose logarithm is a convex function.
References in periodicals archive ?
Mond, Integral inequilities of Hermite-Hadamard type for log-convex functions, Demonst.
Pachpatte, A note on integral inequalities involving two log-convex functions, Math.
M}]-curves for non-quasianalytic, strongly log-convex weight sequences M of moderate growth.
M)] such that M is strongly log-convex and has moderate growth admit a convenient setting, no matter if M is quasianalytic or not.
is log-convex in the Jensen sense on I, if and only if
It follows that a positive function is log-convex in the Jensen sense if and only if it is 2-exponentially convex in the Jensen sense.
Contributors here take the task on, with papers on such aspects as the maximal characterization of Hardy-Sobolev spaces on manifolds, approximately Gaussian marginals and the hyperplane conjecture, on the existence of sub-Gaussian directions for log-concave measures, isoperimetric bounds on convex manifolds, and the log-convex density conjecture.
We note that 0-convex function is simply log-convex function and 1-convex function is ordinary convex function.
If r = 0 and p [not equal to] 0, then f is log-convex, it follows from (1) and (2) that
Niculescu, The Hermite-Hadamard inequality for log-convex functions, Nonlinear Anal.
i[phi]] (v - u) = v - u, the [phi]-convex set K becomes the convex set and consequently, [phi]-convex, [phi]-invex, and log-[phi]-invex functions reduce to convex and log-convex functions.
Keywords and Phrases: Ostrowski inequality, Gruss inequality, Cebysev inequality, Convex functions, Log-convex functions.
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