This article is cited in 1 paper

Further results on Jensen-type inequalities

B. Moosavi^a, H. R. Moradi^b, M. Shah Hosseini<sup>c

a</sup> Department of Mathematics, Safadasht Branch, Islamic Azad University, Tehran, Iran
^b Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran
^c Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran

Abstract: 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.

UDC: 517.38, 517.51

MSC: Primary 47A63, Secondary 26A51, 26D15, 26B25, 39B62} \keywords{Jensen's inequality, convex function, synchronous (asynchronous) function, self-adjoint operator

Received: 28.05.2019
Revised: 21.07.2019
Accepted: 18.07.2019

Language: English

DOI: 10.15393/j3.art.2019.6350

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