Refinements of the Heron and Heinz means inequalities for matrices

Ali, Ilyas; Yang, Hu; Shakoor, Abdul

doi:10.7153/jmi-08-06

Cited by 5 publications

(3 citation statements)

References 3 publications

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“…Kittaneh and Krnić in [11] obtained the some refinements of the left and right inequalities in (4.1) for ν ∈ [0, 1] − { 1 2 }, as follows:…”

Section: Improved Heinz Operator Inequalitiesmentioning

confidence: 99%

“…(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%

“…The aim of this paper is to obtain refinements of the HermiteHadamard inequality (1.8) in the setting of operators (see Theorem (2)). We also present a generalization of the difference version of Heinz inequality (see Theorem (1)). At the end, we study the Heinz operator inequalities, which were proved in [10] and give a series of refinements of these operator inequalities (see Theorem (4) and ( 5)).…”

Section: Introductionmentioning

confidence: 99%

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Refined Heinz operator inequalities and norm inequalities

Ghazanfari¹

2020

Preprint

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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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“…Kittaneh and Krnić in [11] obtained the some refinements of the left and right inequalities in (4.1) for ν ∈ [0, 1] − { 1 2 }, as follows:…”

Section: Improved Heinz Operator Inequalitiesmentioning

confidence: 99%

“…(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%

Section: Introductionmentioning

confidence: 99%

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Refined Heinz operator inequalities and norm inequalities

Ghazanfari¹

2020

Preprint

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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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Norm inequalities for Heinz and Heron means via contractive maps

Ghazanfari

Sababheh

2022

Int. J. Math.

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In this paper, using the contractive maps, we present some new interpolations between the Heinz and Heron operator means for unitarily invariant norms. Let [Formula: see text] and [Formula: see text] be two positive definite operators. and let [Formula: see text], [Formula: see text]. If [Formula: see text] and [Formula: see text], or if [Formula: see text] and [Formula: see text], then [Formula: see text] [Formula: see text] We also consider some Heinz-type inequalities that involve differences and sums of operators. We give new forms and reverse inequalities of the presented inequalities by Singh et al.

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Refinements of the Heron and Heinz means inequalities for matrices

Cited by 5 publications

References 3 publications

Refined Heinz operator inequalities and norm inequalities

Refined Heinz operator inequalities and norm inequalities

Norm Inequalities Related to the Heron and Heinz Means

Norm inequalities for Heinz and Heron means via contractive maps

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