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FUNCTIONAL VERSIONS OF SOME REFINED AND REVERSED OPERATOR MEAN INEQUALITIES

Part of: General theory of linear operators Miscellaneous applications of functional analysis

Published online by Cambridge University Press:  10 August 2017

MUSTAPHA RAÏSSOULI Open the ORCID record for MUSTAPHA RAÏSSOULI [Opens in a new window]
MUSTAPHA RAÏSSOULI*
Affiliation:
Department of Mathematics, Science Faculty, Taibah University, Al Madinah Al Munawwarah, P.O. Box 30097, Zip Code 41477, Saudi Arabia Department of Mathematics, Faculty of Science, Moulay Ismail University, Meknes, Morocco email raissouli.mustapha@gmail.com
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Abstract

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We present refined and reversed inequalities for the weighted arithmetic mean–harmonic mean functional inequality. Our approach immediately yields the related operator versions in a simple and fast way. We also give some operator and functional inequalities for three or more arguments. As an application, we obtain a refined upper bound for the relative entropy involving functional arguments.

Keywords

convex functionoperator meanfunctional meanmean inequalities

MSC classification

Primary: 47A63: Operator inequalities
Secondary: 47A64: Operator means, shorted operators, etc. 46N10: Applications in optimization, convex analysis, mathematical programming, economics
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 3 , December 2017 , pp. 496 - 503
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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