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<p>We extend the classical Grüss inequality from Euclidean disks in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb{R}}^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> to generalized <i>p</i>-disks and present rigorous formulations for functions satisfying Hölder-type conditions. Several new Grüss-type inequalities are established and applied to establish bounds for the covariance of random variables defined either by probability density functions or by joint distributions.</p>

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On the Grüss Type Inequalities Within p-Disks with Applications

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • Mohammad W. Alomari

摘要

We extend the classical Grüss inequality from Euclidean disks in \({\mathbb{R}}^{2}\) R 2 to generalized p-disks and present rigorous formulations for functions satisfying Hölder-type conditions. Several new Grüss-type inequalities are established and applied to establish bounds for the covariance of random variables defined either by probability density functions or by joint distributions.