An integral representation for the weighted geometric mean and its applications

Authors
Qi, Feng Zhang, Xiao Jing Li, Wen Hui
Citation
Qi, Feng et al., An integral representation for the weighted geometric mean and its applications, Acta mathematica Sinica. English series (Print) , 30(1), 2014, pp. 61-68
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
30
Issue
1
Year of publication
2014
Pages
61 - 68
Database
ACNP
SICI code
Abstract
By virtue of Cauchy.s integral formula in the theory of complex functions, the authors establish an integral representation for the weighted geometric mean, apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function, and find a new proof of the well-known weighted arithmetic-geometric mean inequality.