Comptes Rendus
no. 5
Mathematical analysis/Functional analysis
Reverses of operator Aczél inequality
[Inégalités inverses aux inégalités d'Aczél pour les opérateurs]

Présenté par : the Editorial Board

Venus Kaleibary1 ; Shigeru Furuichi2
1 Department of Engineering, Basic Sciences Group, University of Science and Culture, Tehran, Iran
2 Department of Computer Science and System Analysis, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo 156-8550, Japan
Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 475-481.

Nous présentons dans cette Note des inégalités faisant intervenir des fonctions décroissantes sur les opérateurs et des moyennes d'opérateurs. Ces inégalités fournissent des inverses aux inégalités d'Aczél pour les opérateurs dans le cas des moyennes géométriques pondérées.

In this paper, we present some inequalities involving operator decreasing functions and operator means. These inequalities provide some reverses of the operator Aczél inequality dealing with the weighted geometric mean.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.04.005
Venus Kaleibary 1 ; Shigeru Furuichi 2

1 Department of Engineering, Basic Sciences Group, University of Science and Culture, Tehran, Iran
2 Department of Computer Science and System Analysis, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo 156-8550, Japan 
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Venus Kaleibary; Shigeru Furuichi. Reverses of operator Aczél inequality. Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 475-481. doi : 10.1016/j.crma.2018.04.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.04.005/

[1] J. Aczél Some general methods in the theory of functional equations in one variable. New applications of functional equations, Usp. Mat. Nauk (N.S.), Volume 11 (1956), pp. 3-68 (in Russian)

[2] T. Ando; F. Hiai Operator log-convex functions and operator means, Math. Ann., Volume 350 (2011), pp. 611-630

[3] R. Bhatia Matrix Analysis, Grad. Texts Math., vol. 169, Springer-Verlag, 1997

[4] J.-C. Bourin; E.-Y. Lee; M. Fujii; Y. Seo A matrix reverse Hölder inequality, Linear Algebra Appl., Volume 431 (2009), pp. 2154-2159

[5] Y.J. Cho; M. Matić; J. Pečarić Improvements of some inequalities of Aczél's type, J. Math. Anal. Appl., Volume 259 (2001), pp. 226-240

[6] S.S. Dragomir A generalization of Aczél's inequality in inner product spaces, Acta Math. Hung., Volume 65 (1994), pp. 141-148

[7] S.S. Dragomir On new refinements and reverses of Young's operator inequality, RGMIA Res. Rep. Collect., Volume 18 (2015) http://rgmia.org/papers/v18/v18a135.pdf (Art. 135)

[8] S. Furuichi Further improvements of Young inequality, RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. (2017) | DOI

[9] S. Furuichi; H.R. Moradi Some refinements of classical inequalities, Rocky Mt. J. Math. (2018) (in press) | arXiv

[10] T. Furuta; J. Mićić; J.E. Pečarić; Y. Seo Mond–Pečarić Method in Operator Inequalities, Monogr. Inequal., vol. 1, Element, Zagreb, 2005

[11] M.B. Ghaemi; V. Kaleibary Some inequalities involving operator monotone functions and operator means, Math. Inequal. Appl., Volume 19 (2016), pp. 757-764

[12] W. Liao; J. Wu; J. Zhao New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant, Taiwan. J. Math., Volume 19 (2015), pp. 467-479

[13] M.S. Moslehian Operator Aczél inequality, Linear Algebra Appl., Volume 434 (2011), pp. 1981-1987

[14] T. Popoviciu On an inequality, Gaz. Mat. Fiz., Ser. A, Volume 11 (1959), pp. 451-461 (in Romanian)

[15] W. Specht Zur Theorie der elementaren Mittel, Math. Z., Volume 74 (1960), pp. 91-98

[16] J. Tian; W.-L. Wang Generalizations of refined Hölder's inequalities and their applications, Math. Probl. Eng., Volume 2014 (2014)

[17] M. Tominaga Specht's ratio in the Young inequality, Sci. Math. Jpn., Volume 55 (2002), pp. 583-588

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