Further Accurate Numerical Radius Inequalities

Qawasmeh, Tariq; Qazza, Ahmad; Hatamleh, Raed; Alomari, Mohammad W.; Saadeh, Rania

doi:10.3390/axioms12080801

Cited by 3 publications

(2 citation statements)

References 42 publications

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“…For example, it is well known that the spectrum of an operator is contained in the closure of its numerical range. For basic properties numerical radius, we refer to (Alomari, 2021), (Aici et al, 2023), (Bhunia and Paul, 2021), , (Dragomir, 2009), (Gustanson and Rao, 1997), (Jana et al, 2023), (Kian, 2014), (Kian and Alomari, 2022), (Qawasmeh et al, 2023).…”

Section: 𝑏𝑒𝑟(𝑇) ≤ 𝑤(𝑇)mentioning

confidence: 99%

More Correct Berezin Symbol Inequalities

Başaran,

Gurdal

2023

dngcrj

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The purpose of this research is to show bounds for some Berezin number inequalities in an innovative approach. Some inequalities have been proven using the improvement of the Hermite-Hadamard inequality. These inequalities are a refined version of Huban et al.'s inequalities (Huban et al., 2021b; Huban et al., 2022a) and Başaran et al.'s inequalities (Başaran et al., 2022). Finally, we prove last three theorems by applying the method of Cartesian decomposition.

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Section: 𝑏𝑒𝑟(𝑇) ≤ 𝑤(𝑇)mentioning

confidence: 99%

More Correct Berezin Symbol Inequalities

Başaran,

Gurdal

2023

dngcrj

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“…Consequently, researchers have dedicated considerable efforts to finding better bounds for more accurate approximations and a deeper understanding of these relationships. For more information on norm and numerical radius inequalities, readers are encouraged to consult the following references [15][16][17][18][19][20][21][22][23][24][25][26] and the additional references cited therein.…”

Section: Introduction and Preliminarymentioning

confidence: 99%

Hölder-Type Inequalities for Power Series of Operators in Hilbert Spaces

Altwaijry,

Dragomir,

Feki

2024

Axioms

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Consider the power series with complex coefficients h(z)=∑k=0∞akzk and its modified version ha(z)=∑k=0∞|ak|zk. In this article, we explore the application of certain Hölder-type inequalities for deriving various inequalities for operators acting on the aforementioned power series. We establish these inequalities under the assumption of the convergence of h(z) on the open disk D(0,ρ), where ρ denotes the radius of convergence. Additionally, we investigate the norm and numerical radius inequalities associated with these concepts.

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An application of Hayashi's inequality in numerical integration

Heilat,

Qazza,

Hatamleh

et al. 2023

Open Mathematics

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This study systematically develops error estimates tailored to a specific set of general quadrature rules that exclusively incorporate first derivatives. Moreover, it introduces refined versions of select generalized Ostrowski’s type inequalities, enhancing their applicability. Through the skillful application of Hayashi’s celebrated inequality to specific functions, the provided proofs underpin these advancements. Notably, this approach extends its utility to approximate integrals of real functions with bounded first derivatives. Remarkably, it employs Newton-Cotes and Gauss-Legendre quadrature rules, bypassing the need for stringent requirements on higher-order derivatives.

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Further Accurate Numerical Radius Inequalities

Cited by 3 publications

References 42 publications

More Correct Berezin Symbol Inequalities

More Correct Berezin Symbol Inequalities

Hölder-Type Inequalities for Power Series of Operators in Hilbert Spaces

An application of Hayashi's inequality in numerical integration

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