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


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.


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

Mathematics Subject Classification

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



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.


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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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