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Afrika Matematika

, Volume 26, Issue 7–8, pp 1253–1262 | Cite as

On the degree of the weighted geometric mean as a complete Bernstein function

  • Bai-Ni GuoEmail author
  • Feng Qi
Article
First Online:

Abstract

In the paper, the authors verify that the geometric mean of many positive numbers is a complete Bernstein function of degree \(0\) and, consequently, a positive operator monotone function.

Keywords

Geometric mean Completely monotonic function Completely monotonic degree Complete Bernstein function Operator monotone function 

Mathematics Subject Classification

Primary 26E60 Secondary 26A48 30E20 44A10 44A20 
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Notes

Acknowledgments

The authors heartily express their thanks to the anonymous referee for his/her very helpful corrections and very valuable suggestions to the original version of this paper.

References

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Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Mathematics and InformaticsHenan Polytechnic UniversityJiaozuoChina
  2. 2.Department of Mathematics, College of ScienceTianjin Polytechnic UniversityTianjinChina

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