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Open AccessArticle

Integral Inequalities of Chebyshev Type for Continuous Fields of Hermitian Operators Involving Tracy–Singh Products and Weighted Pythagorean Means

Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
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Symmetry 2019, 11(10), 1256; https://doi.org/10.3390/sym11101256
Received: 14 August 2019 / Revised: 23 September 2019 / Accepted: 5 October 2019 / Published: 9 October 2019
(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Applications)
In this paper, we establish several integral inequalities of Chebyshev type for bounded continuous fields of Hermitian operators concerning Tracy-Singh products and weighted Pythagorean means. The weighted Pythagorean means considered here are parametrization versions of three symmetric means: the arithmetic mean, the geometric mean, and the harmonic mean. Every continuous field considered here is parametrized by a locally compact Hausdorff space equipped with a finite Radon measure. Tracy-Singh product versions of the Chebyshev-Grüss inequality via oscillations are also obtained. Such integral inequalities reduce to discrete inequalities when the space is a finite space equipped with the counting measure. Moreover, our results include Chebyshev-type inequalities for tensor product of operators and Tracy-Singh/Kronecker products of matrices. View Full-Text
Keywords: Chebyshev inequality; Tracy-Singh product; continuous field of operators; Bochner integral; weighted Pythagorean mean Chebyshev inequality; Tracy-Singh product; continuous field of operators; Bochner integral; weighted Pythagorean mean
MDPI and ACS Style

Ploymukda, A.; Chansangiam, P. Integral Inequalities of Chebyshev Type for Continuous Fields of Hermitian Operators Involving Tracy–Singh Products and Weighted Pythagorean Means. Symmetry 2019, 11, 1256.

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