Feng Qi, Xiao-Jing Zhang, Wen-Hui Li
Published 2013-01-29Version 1
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 $n$ 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.
Comments: 10 pages
Journal: Feng Qi, Xiao-Jing Zhang, and Wen-Hui Li, L\'evy-Khintchine representation of the geometric mean of many positive numbers and applications, Mathematical Inequalities & Applications 17 (2014), no. 2, 719--729
Some Bernstein functions and integral representations concerning harmonic and geometric means
Integral representation of some functions related to the Gamma function
A new proof of the geometric-arithmetic mean inequality by Cauchy's integral formula
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