The geometric mean is a Bernstein function
Classical Analysis and ODEs
2014-03-07 v1 Complex Variables
Abstract
In the paper, the authors establish, by using Cauchy integral formula in the theory of complex functions, an integral representation for the geometric mean of positive numbers. From this integral representation, the geometric mean is proved to be a Bernstein function and a new proof of the well known AG inequality is provided.
Cite
@article{arxiv.1301.6848,
title = {The geometric mean is a Bernstein function},
author = {Feng Qi and Xiao-Jing Zhang and Wen-Hui Li},
journal= {arXiv preprint arXiv:1301.6848},
year = {2014}
}
Comments
10 pages