logarithmically convex function
It is easy to see that a logarithmically convex function is a convex function, but the converse is not true. For example is a convex function, but is not a convex function and thus is not logarithmically convex. On the other hand is logarithmically convex since is convex. A less trivial example of a logarithmically convex function is the gamma function, if restricted to the positive reals.
The definition is easily extended to functions , for any connected set (where still we have ), in the obvious way. Such a function is logarithmically convex if it is logarithmically convex on all intervals .
- 1 John B. Conway. . Springer-Verlag, New York, New York, 1978.
|Title||logarithmically convex function|
|Date of creation||2013-03-22 14:13:33|
|Last modified on||2013-03-22 14:13:33|
|Last modified by||jirka (4157)|
|Synonym||log convex function|