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arXiv:1303.3122 [math.CA]AbstractReferencesReviewsResources

Integral representations of the weighted geometric mean and the logarithmic mean

Feng Qi, Xiao-Jing Zhang, Wen-Hui Li

Published 2013-03-13Version 1

In the paper, the authors show that the weighted geometric mean and the logarithmic mean are Bernstein functions and establish integral representations of these means by Cauchy's integral theorem in the theory of complex functions.

Comments: 12 pages. arXiv admin note: text overlap with arXiv:1301.6848
Journal: Feng Qi, Xiao-Jing Zhang, and Wen-Hui Li, L\'evy-Khintchine representations of the weighted geometric mean and the logarithmic mean, Mediterranean Journal of Mathematics 11 (2014), no. 2, 315--327
Categories: math.CA, math.CV
Subjects: 26E60, 30E20, 26A48, 44A20
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