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<p>In this paper, we establish a new refinement of Hermite-Hadamard-type inequalities for <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3327_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>p</mi> <mo>−</mo> <mi>q</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(p-q) $</EquationSource> </InlineEquation>-convex functions. By the definition of suitable functions, we extend this refinement to operator <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3327_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>p</mi> <mo>−</mo> <mi>q</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(p-q) $</EquationSource> </InlineEquation>-convex functions associated with commutative operators. Additionally, we provide several examples to illustrate our results.</p>

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A new refinement of the Hermite-Hadamard type inequalities for operator \((p-q) \)-convex functions

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  • 发表日期：

    2025年6月12日

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  • Gholamreza Zabandan,
  • Farideh Tahmasbnia

摘要

In this paper, we establish a new refinement of Hermite-Hadamard-type inequalities for ( p − q ) $(p-q) $ -convex functions. By the definition of suitable functions, we extend this refinement to operator ( p − q ) $(p-q) $ -convex functions associated with commutative operators. Additionally, we provide several examples to illustrate our results.