Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-28T14:29:59.323Z Has data issue: false hasContentIssue false
  • English
  • Français

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 [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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. 

References

Dragomir, S. S., ‘Bounds of the normalised Jensen’s functional’, Bull. Aust. Math. Soc. 74(3) (2006), 471–478.CrossRefGoogle Scholar
Dragomir, S. S., ‘Some inequalities for weighted harmonic and arithmetic operator means’, RGMIA 19 (2016), Art. 5, 10 pages.Google Scholar
Fujii, J. I. and Kamei, E., ‘Relative operator entropy in noncommutative information theory’, Math. Japonica 34 (1989), 341–348.Google Scholar
Fujii, J. I. and Seo, Y., ‘Tsallis relative operator entropy with negative parameters’, Adv. Oper. Theory 1(2) (2016), 219–235.Google Scholar
Furuichi, S., ‘Inequalities for Tsallis relative entropy and generalized skew information’, Linear Multilinear Algebra 59(10) (2011), 1143–1158.Google Scholar
Furuta, T., ‘Parameteric extensions of Shannon inequality and its reverse one in Hilbert space operators’, Linear Algebra Appl. 381 (2004), 219–235.Google Scholar
Hirzallah, O., Kittaneh, F., Krnić, M., Lovričenvić, N. and Pečarić, J., ‘Refinements and reverses of means inequalities for Hilbert space operators’, Banach J. Math. Anal. 7(2) (2013), 15–29.Google Scholar
Kittaneh, F., Krnić, M., Lovrčenvić, N. and Pečarić, J., ‘Improved arithmetic–geometric and Heinz means inequalities for Hilbert space operators’, Publ. Math. Debrecen 80(3–4) (2012), 465–478.Google Scholar
Moslehian, M. S., Mirzapour, F. and Morassaei, A., ‘Operator entropy inequalities’, Colloq. Math. 130 (2013), 159–168.Google Scholar
Raïssouli, M., ‘Relative functional entropy in convex analysis’, J. Appl. Anal. 17 (2011), 231–239.Google Scholar
Raïssouli, M., ‘Functional versions for some operator entropy inequalities’, Ann. Funct. Anal. 6(2) (2015), 204–211.Google Scholar
Zuo, G., Shi, G. and Fujii, M., ‘Refined Young inequality with Kantorovich constant’, J. Math. Inequal. 5 (2011), 551–556.Google Scholar