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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 4

Some generalizednumerical radius inequalities involving Kwong functions

Mojtaba Bakherad
Pages
951–958
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Among other inequalities, it is shown that if $X$ is an arbitrary $ntimes n$ matrix and $A,B$ are positive semidefinite, then[ omega(H_{f,g}(A))leq k, omega(AX+XA), ] which is equivalent to[omegabig(H_{f,g}(A,B)pm H_{f,g}(B,A)big)leq k',left{omega((A+B)X+X(A+B))+omega((A-B)X-X(A-B))right},] where $f$ and $g$ are two continuous functions on $(0,infty)$ such that $h(t)={f(t)over g(t)}$ is Kwong, $k=maxleft{{f(lambda)g(lambda)over lambda}: {lambdainsigma(A)}right}$ and $k'=maxleft{{f(lambda)g(lambda)over lambda}: {lambdainsigma(A)cupsigma(B)}right}$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We prove several numerical radius inequalities involving positive semidefinite matrices via the Hadamard product and Kwong functions.
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Key Findings & Data:We prove several numerical radius inequalities involving positive semidefinite matrices via the Hadamard product and Kwong functions.
💡
Conclusion & Impact:Among other inequalities, it is shown that if $X$ is an arbitrary $ntimes n$ matrix and $A,B$ are positive semidefinite, then[ omega(H_{f,g}(A))leq k, omega(AX+XA), ] which is equivalent to[omegabig(H_{f,g}(A,B)pm H_{f,g}(B,A)big)leq k',left{omega((A+B)X+X(A+B))+omega((A-B)X-X(A-B))right},] where $f$ and $g$ are two continuous functions on $(0,infty)$ such that $h(t)={f(t)over g(t)}$ is Kwong, $k=maxleft{{f(lambda)g(lambda)over lambda}: {lambdainsigma(A)}right}$ and $k'=maxleft{{f(lambda)g(lambda)over lambda}: {lambdainsigma(A)cupsigma(B)}right}$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We prove several numerical radius inequalities involving positive semidefinite matrices via the Hadamard product and Kwong functions. Among other inequalities, it is shown that if $X$ is an arbitrary $ntimes n$ matrix and $A,B$ are positive semidefinite, then[ omega(H_{f,g}(A))leq k, omega(AX+XA), ] which is equivalent to[omegabig(H_{f,g}(A,B)pm H_{f,g}(B,A)big)leq k',left{omega((A+B)X+X(A+B))+omega((A-B)X-X(A-B))right},] where $f$ and $g$ are two continuous functions on $(0,infty)$ such that $h(t)={f(t)over g(t)}$ is Kwong, $k=maxleft{{f(lambda)g(lambda)over lambda}: {lambdainsigma(A)}right}$ and $k'=maxleft{{f(lambda)g(lambda)over lambda}: {lambdainsigma(A)cupsigma(B)}right}$.

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Cite This Article

Bakherad, M. (2022). Some generalizednumerical radius inequalities involving Kwong functions. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 4, 951–958. https://ajindex.com/articles/529756

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