Further Inequalities for the Weighted Numerical Radius of Operators

Altwaijry, Najla; Feki, Kais; Minculete, Nicuşor

doi:10.3390/math10193576

Cited by 9 publications

(7 citation statements)

References 32 publications

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“…Interested readers can establish the fascinating results on different class of convex and generalized functions. The results can be generalized to different fields such as fractional calculus, q-calculus, interval-valued, and time-scale domains for the square operator modulus in semi Hilbert spaces (see, for example [15,22]).…”

Section: Discussionmentioning

confidence: 99%

Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions

Mehmood

Srivástava

Mohammed

et al. 2022

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In this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fejér type for operator ω1,ω2-preinvex functions. The bounds for both left-hand and right-hand sides of the integral inequality are established for operator ω1,ω2-preinvex functions of the positive self-adjoint operator in the complex Hilbert spaces. We give the special cases to our results; thus, the established results are generalizations of earlier work. In the last section, we give applications for synchronous (asynchronous) functions.

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Section: Discussionmentioning

confidence: 99%

Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions

Mehmood

Srivástava

Mohammed

et al. 2022

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“…(1) Notice that the inequalities in (2.23) are already proved by the second author in [18] and by Altwaijry et al in [1]. However, the techniques used here are different from the other proofs.…”

Section: Theorem 225 Let T S ∈ Bmentioning

confidence: 92%

Inequalities for the $A$-joint numerical radius of two operators and their applications

Feki

2024

Hacettepe Journal of Mathematics and Statistics

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Let $\big(\mathcal{H}, \langle \cdot, \cdot\rangle \big)$ be a complex Hilbert space and $A$ be a positive (semidefinite) bounded linear operator on $\mathcal{H}$. The semi-inner product induced by $A$ is given by ${\langle x, y\rangle}_A := \langle Ax, y\rangle$, $x, y\in\mathcal{H}$ and defines a seminorm ${\|\cdot\|}_A$ on $\mathcal{H}$. This makes $\mathcal{H}$ into a semi-Hilbert space. The $A$-joint numerical radius of two $A$-bounded operators $T$ and $S$ is given by \begin{align*} \omega_{A,\text{e}}(T,S) = \sup_{\|x\|_A= 1}\sqrt{\big|{\langle Tx, x\rangle}_A\big|^2+\big|{\langle Sx, x\rangle}_A\big|^2}. \end{align*} In this paper, we aim to prove several bounds involving $\omega_{A,\text{e}}(T,S)$. This allows us to establish some inequalities for the $A$-numerical radius of $A$-bounded operators. In particular, we extend the well-known inequalities due to Kittaneh [Studia Math. 168 (2005), no. 1, 73-80]. Moreover, several bounds related to the $A$-Davis-Wielandt radius of semi-Hilbert space operators are also provided.

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“…Taking the supremum over all unit vector u ∈ G , we obtain the desired result. The third inequality follows by applying (17) to the second term in the second inequality.…”

Section: Corollary 2 Letmentioning

confidence: 99%

“…The constant 1 32 is the best possible. For more generalizations and recent related results concerning numerical radius, the reader may refer to [9][10][11][12][13][14][15][16][17][18][19] and the references therein. In addition, a survey of the numerical radius can be found in [20].…”

Section: Introductionmentioning

confidence: 99%

On Further Refinements of Numerical Radius Inequalities

Hazaymeh,

Qazza,

Hatamleh

et al. 2023

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This paper introduces several generalized extensions of some recent numerical radius inequalities of Hilbert space operators. More preciously, these inequalities refine the recent inequalities that were proved in literature. It has already been demonstrated that some inequalities can be improved or restored by concatenating some into one inequality. The main idea of this paper is to extend the existing numerical radius inequalities by providing a unified framework. We also present a numerical example to demonstrate the effectiveness of the proposed approach. Roughly, our approach combines the existing inequalities, proved in literature, into a single inequality that can be used to obtain improved or restored results. This unified approach allows us to extend the existing numerical radius inequalities and show their effectiveness through numerical experiments.

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Further Inequalities for the Weighted Numerical Radius of Operators

Cited by 9 publications

References 32 publications

Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions

Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions

Inequalities for the $A$-joint numerical radius of two operators and their applications

On Further Refinements of Numerical Radius Inequalities

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