numbers, then is logarithmically convex.

If is any family of logarithmically convex functions, then is logarithmically convex.

If is convex and is logarithmically convex and non-decreasing, then is logarithmically convex.

Properties

A logarithmically convex function f is a convex function since it is the composite of the increasing convex function and the function , which is by definition convex. However, being logarithmically

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