On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities

Alomari, Mohammad W.; Bercu, Gabriel; Chesneau, Christophe

doi:10.3390/sym14071432

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…The equality in ( 12) holds if the vectors BAx and C * D * y are linearly dependent in H . For other closely related versions of Kato's inequality and its refinements, see [1,3,10,28,[34][35][36][37][38].…”

Section: Lemma 2 (The Mccarthy Inequality) [30]mentioning

confidence: 99%

On Some Inequalities for the Generalized Euclidean Operator Radius

Alomari

Bercu

Chesneau

et al. 2023

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In the literature, there are many criteria to generalize the concept of a numerical radius; one of the most recent and interesting generalizations is the so-called generalized Euclidean operator radius, which reads: ωpT1,⋯,Tn:=supx=1∑i=1nTix,xp1/p,p≥1, for all Hilbert space operators T1,⋯,Tn. Simply put, it is the numerical radius of multivariable operators. This study establishes a number of new inequalities, extensions, and generalizations for this type of numerical radius. More precisely, by utilizing the mixed Schwarz inequality and the extension of Furuta’s inequality, some new refinement inequalities are obtained for the numerical radius of multivariable Hilbert space operators. In the case of n=1, the resulting inequalities could be considered extensions and generalizations of the classical numerical radius.

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Section: Lemma 2 (The Mccarthy Inequality) [30]mentioning

confidence: 99%

On Some Inequalities for the Generalized Euclidean Operator Radius

Alomari

Bercu

Chesneau

et al. 2023

Axioms

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“…These concepts are used in different parts of mathematics. Previous research, including the studies referenced in [1][2][3][4][5][6][7][8][9][10], has extensively investigated mathematical inequalities and discovered significant findings. These studies provide a foundation for future research in this field.…”

Section: Introduction and Preliminarymentioning

confidence: 99%

Norm and Numerical Radius Inequalities for Sums of Power Series of Operators in Hilbert Spaces

Altwaijry,

Dragomir,

Feki

2024

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The main focus of this paper is on establishing inequalities for the norm and numerical radius of various operators applied to a power series with the complex coefficients h(λ)=∑k=0∞akλk and its modified version ha(λ)=∑k=0∞|ak|λk. The convergence of h(λ) is assumed on the open disk D(0,R), where R is the radius of convergence. Additionally, we explore some operator inequalities related to these concepts. The findings contribute to our understanding of operator behavior in bounded operator spaces and offer insights into norm and numerical radius inequalities.

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Some Refinements of the Tensorial Inequalities in Hilbert Spaces

et al. 2023

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Hermite–Hadamard inequalities and their refinements have been investigated for a long period of time. In this paper, we obtained refinements of the Hermite–Hadamard inequality of tensorial type for the convex functions of self-adjoint operators in Hilbert spaces. The obtained inequalities generalize the previously obtained inequalities by Dragomir. We also provide useful Lemmas which enabled us to obtain the results. The examples of the obtained inequalities for specific convex functions have been given in the example and consequences section. Symmetry in the upper and lower bounds can be seen in the last Theorem of the paper given, as the upper and lower bounds differ by a constant.

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On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities

Cited by 3 publications

References 33 publications

On Some Inequalities for the Generalized Euclidean Operator Radius

On Some Inequalities for the Generalized Euclidean Operator Radius

Norm and Numerical Radius Inequalities for Sums of Power Series of Operators in Hilbert Spaces

Some Refinements of the Tensorial Inequalities in Hilbert Spaces

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