Geodesic
Further results on Jensen-type inequalities
Problemy analiza, Tome 8 (2019) no. 3, pp. 112-124.

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In this paper, we establish some Jensen-type inequalities for continuous functions of self-adjoint operators on complex Hilbert spaces. Furthermore, using the Cartesian decomposition of an operator, we improve the known result due to Mond and Pečarić. Some refinements of the Hölder–McCarthy inequality are given as well.
Keywords: Jensen's inequality, convex function, synchronous (asynchronous) function, self-adjoint operator. 
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B. Moosavi; H. R. Moradi; M. Shah Hosseini. Further results on Jensen-type inequalities. Problemy analiza, Tome 8 (2019) no. 3, pp. 112-124. http://geodesic.mathdoc.fr/item/PA_2019_8_3_a10/

[1] Bourin J.-C., “Some inequalities for norms on matrices and operators”, Linear Algebra Appl., 292 (1999), 139–154 | DOI | MR | Zbl

[2] Choi M. D., “A Schwarz inequality for positive linear maps on $C^*$–algebras”, Illinois J. Math., 18:4 (1974), 565–574 | DOI | MR | Zbl

[3] Davis C., “A Schwarz inequality for convex operator functions”, Proc. Amer. Math. Soc., 8 (1957), 42–44 | DOI | MR | Zbl

[4] Dragomir S. S., “A weakened version of Davis–Choi–Jensen's inequality for normalised positive linear maps”, Proyecciones, 36:1 (2017), 81–94 | DOI | MR | Zbl

[5] Dragomir S. S., “Čebyšev's type inequalities for functions of selfadjoint operators in Hilbert spaces”, Linear Multilinear Algebra, 58:7 (2010), 805–814 | DOI | MR | Zbl

[6] Fujii J.-I., “A trace inequality arising from quantum information theory”, Linear Algebra Appl., 400 (2005), 141–146 | DOI | MR | Zbl

[7] Hansen F., Pečarić J., Perić I., “Jensen's operator inequality and it's converses”, Math. Scand., 100:1 (2007), 61–73 | DOI | MR | Zbl

[8] Horváth L., Khan K. A., Pečarić J., “Cyclic refinements of the different versions of operator Jensen's inequality”, Electron. J. Linear Algebra, 31 (2016), 125–133 | DOI | MR | Zbl

[9] Mićić J., Moradi H. R., Furuichi S., “Choi–Davis–Jensen's inequality without convexity”, J. Math. Inequal., 12:4 (2018), 1075–1085 | DOI | MR | Zbl

[10] Mićić J., Pečarić J., “Some mappings related to Levinson's inequality for Hilbert space operators”, Filomat., 31:7 (2017), 1995–2009 | DOI | MR

[11] Mond B., Pečarić J., “On Jensen's inequality for operator convex functions”, Houston J. Math., 21 (1995), 739–754 | MR | Zbl

[12] Moradi H. R., Furuichi S., Mitroi F. C., Naseri R., “An extension of Jensen's operator inequality and its application to Young inequality”, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., 113:2 (2019), 605–614 | DOI | MR | Zbl

[13] Moradi H. R., Omidvar M. E., Adil Khan M., Nikodem K., “Around Jensen's inequality for strongly convex functions”, Aequat. Math., 92:1 (2018), 25–37 | DOI | MR | Zbl

[14] Moradi H. R., Omidvar M. E., Dragomir S. S., “An operator extension of Čebyšev inequality”, An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat., 25:2 (2017), 135–147 | DOI | MR | Zbl