The Hasegawa-Petz mean: properties and inequalities. (English) Zbl 1239.26019
Summary: We study a family of means introduced by H. Hasegawa and D. Petz [Lett. Math. Phys. 38, No. 2, 221–225 (1996; Zbl 0855.58070)]. Properties with respect to the parameter, such as monotonicity and logarithmic concavity, further, monotonicity and concavity in the mean variables are shown. Besides, the comparison between the Hasegawa-Petz mean and the geometric mean is completely solved. The connection to earlier results on operator monotonicity and some applications are also discussed.
MSC:
| 26E60 | Means |
| 26D07 | Inequalities involving other types of functions |
| 58Z05 | Applications of global analysis to the sciences |
Keywords:
Hasegawa-Petz mean; monotonicity; concavity; comparison; Stolarsky mean; operator monotone functionCitations:
Zbl 0855.58070References:
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