Operator mean inequalities and Kwong functions

In this paper, we study operator mean inequalities for the weighted arithmetic, geometric, and harmonic means. We give a slight modification of Audenaert’s result to show the relation between Kwong functions and operator monotone functions. Operator mean inequalities provide some analogs of the geom...

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Bibliographic Details
Published in:Archiv der Mathematik 2024-06, Vol.122 (6), p.659-669
Main Authors: Gharakhanlu, Nahid, Moslehian, Mohammad Sal, Najafi, Hamed
Format: Article
Language:English
Subjects:
Concavity
Inequalities
Mathematics
Mathematics and Statistics
Monotone functions
Operators (mathematics)
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Summary:In this paper, we study operator mean inequalities for the weighted arithmetic, geometric, and harmonic means. We give a slight modification of Audenaert’s result to show the relation between Kwong functions and operator monotone functions. Operator mean inequalities provide some analogs of the geometric concavity property for Kwong functions, operator convex, and operator monotone functions. Moreover, we give our points across by way of some examples which show the usage of our main results.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-024-01980-4