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Abstract <p>In this paper, we generalize the classical Ostrowski inequality from the real line to generalized <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8384_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(q\)</EquationSource> <!--LobJMat2560731Alomari-m3--> </InlineEquation>-disks in Minkowski space. By developing a formulation that remains valid in these non-Euclidean settings, we establish a broader framework for the Ostrowski inequality within Minkowski geometry. In particular, we derive several Ostrowski-type inequalities for functions defined on <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8384_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(q\)</EquationSource> <!--LobJMat2560731Alomari-m4--> </InlineEquation>-disks that satisfy certain Hölder-type conditions.</p>

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On the Ostrowski Inequality on \(\boldsymbol{q}\)-Disks

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Mohammad W. Alomari,
  • Christophe Chesneau

摘要

Abstract

In this paper, we generalize the classical Ostrowski inequality from the real line to generalized \(q\) -disks in Minkowski space. By developing a formulation that remains valid in these non-Euclidean settings, we establish a broader framework for the Ostrowski inequality within Minkowski geometry. In particular, we derive several Ostrowski-type inequalities for functions defined on \(q\) -disks that satisfy certain Hölder-type conditions.