Complete interpolation of matrix versions of Heron and Heinz means

Kaur, Rupinderjit; Singh, Mandeep

doi:10.7153/mia-16-06

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…Further in [10], authors proved some generalizations of the difference version of Heinz inequality, given by Remark 3.12]. These results have also been proved in matrix version by several authors; see [12,18] for example. The aim of this paper is to obtain refinements of inequalities (1.3) and (1.4).…”

Section: Introductionmentioning

confidence: 90%

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Norm Inequalities Related to the Heron and Heinz Means

et al. 2017

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In this article, we present several inequalities treating operator means and the Cauchy-Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means, several generalizations of the difference version of the Heinz means and further refinements of the Cauchy-Schwarz inequality. The techniques used to accomplish these results include convexity and Löwner matrices.2010 Mathematics Subject Classification. 47A30, 47A63, 47A64, 15A60.

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Section: Introductionmentioning

confidence: 90%

“…Moreover, it is proved that |||A ν XB 1−ν − A 1−ν XB ν ||| is a convex function of ν; see [10,Remark 3.12]. These results have also been proved in matrix version by several authors; see [12,18] for example. The aim of this paper is to obtain refinements of inequalities (1.3) and (1.4).…”

Section: Introductionmentioning

confidence: 93%

Norm Inequalities Related to the Heron and Heinz Means

et al. 2017

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“…(1.1) R. Kaur and M. Singh [8] have proved that for A, B, X ∈ M n , such that A, B are positive definite, then for any unitarily invariant norm |||.|||, and 1 4…”

Section: Introductionmentioning

confidence: 99%

Refined Heinz operator inequalities and norm inequalities

Ghazanfari¹

2020

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In this article we study the Heinz and Hermite-Hadamard inequalities. We derive the whole series of refinements of these inequalities involving unitarily invariant norms, which improve some recent results, known from the literature.We also prove that if A, B, X ∈ M n (C) such that A and B are positive definite and f is an operator monotone function on (0, ∞). ThenFinally we obtain a series of refinements of the Heinz operator inequalities, which were proved by Kittaneh and Krnić.

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“…Then this inequality was further explored in [8], for example. Our motivation of the current work begins with (1.2).…”

Section: Introductionmentioning

confidence: 99%