The geometric mean is a Bernstein function

Published 29 Jan 2013 in math.CA and math.CV | (1301.6848v1)

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 $n$ 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.

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