An Extension of the AM–GM–HM Inequality

Tan, Fuping; Xie, Antai

doi:10.1007/s41980-019-00253-z

Cited by 16 publications

(5 citation statements)

References 14 publications

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“…where v ∈ [0, 1] and r ∈ [−1, 0]. This improves Tan and Xie's Theorem 2.4 in [22] if setting Φ(X) = X for every X ∈ M n (C) and replacing A by A −1 , B by B −1 , respectively, and r = −1, which is also a special result of Bedrani, Kittaneh and Sababheh's Theorem 4.1 in [4].…”

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confidence: 67%

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Inequalities for sector matrices with negative power

Gao

2021

Filomat

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In this paper, we present some inequalities for sector matrices with negative power. Among other results, we prove that if A,B ? Mn(C) with W(A),W(B) ? S?, then for any positive unital linear map ?, it holds R((1-v)?(A) + v?(B))r ? cos2r(?)R?((1-v)Ar + vBr), where v ? [0,1] and r ? [-1,0]. This improves Tan and Xie?s Theorem 2.4 in [22] if setting ?(X) = X for every X ? Mn(C) and replacing A by A-1, B by B-1, respectively, and r=-1, which is also a special result of Bedrani, Kittaneh and Sababheh?s Theorem 4.1 in [4].

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confidence: 67%

“…Utilizing the weighted geometric mean defined by Raissouli, Moslehian and Furuichi for two accretive matrices, Tan and Xie [22] gave an AM-GM-HM inequality for sectorial matrices as follows.…”

Section: Introductionmentioning

confidence: 99%

Inequalities for sector matrices with negative power

Gao

2021

Filomat

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“…However, we find from the inequality cos 2 α R (A! t B) ≤ R (A∇ t B) that both inequalities above do not improve the known inequality [46]:…”

Section: On the Difference Of Two Perspectivesmentioning

confidence: 87%

Further properties of accretive matrices

Furuichi,

Moradi,

Sababheh

2024

Ann. Fenn. Math.

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To better understand the algebra \(\mathcal{M}_n\) of all \(n\times n\) complex matrices, we explore the class of accretive matrices. This class has received renowned attention in recent years due to its role in complementing those results known for positive definite matrices. Among many results, we present order-preserving results, Choi–Davis-type inequalities, mean-convex inequalities, sub-multiplicative results for the real part, and new bounds of the absolute value of accretive matrices. These results will be compared with the existing literature. In the end, we quickly pass through related entropy results for accretive matrices.

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“…However, we find from the inequality cos 2 α R (A! t B) ≤ R (A∇ t B) that both inequalities above do not improve the known inequality [43]:…”

Section: On the Difference Of Two Perspectivesmentioning

confidence: 87%

Further Properties of Accretive Matrices

Moradi¹,

Furuichi²,

Sababheh³

2022

Preprint

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To better understand the algebra M n of all n×n complex matrices, we explore the class of accretive matrices. This class has received renowned attention in recent years due to its role in complementing those results known for positive definite matrices. More precisely, we have several results that allow a better understanding of accretive matrices. Among many results, we present order-preserving results, Choi-Davis-type inequalities, mean-convex inequalities, sub-multiplicative results for the real part, and new bounds of the absolute value of accretive matrices. These results will be compared with the existing literature. In the end, we quickly pass through related entropy results for accretive matrices.

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An Extension of the AM–GM–HM Inequality

Cited by 16 publications

References 14 publications

Inequalities for sector matrices with negative power

Inequalities for sector matrices with negative power

Further properties of accretive matrices

Further Properties of Accretive Matrices

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