logconvex function

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.

convex function | logarithmically concave function