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.
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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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Guo, BN., Qi, F. On the degree of the weighted geometric mean as a complete Bernstein function. Afr. Mat. 26, 1253–1262 (2015). https://doi.org/10.1007/s13370-014-0279-2
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DOI: https://doi.org/10.1007/s13370-014-0279-2
Keywords
- Geometric mean
- Completely monotonic function
- Completely monotonic degree
- Complete Bernstein function
- Operator monotone function