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<p>The purpose of this study is to introduce new (<i>p</i>,&#xa0;<i>q</i>)-Hermite–Hadamard and (<i>p</i>,&#xa0;<i>q</i>)-Hermite–Hadamard–Fej<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_514_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\acute{e}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>e</mi> <mo>´</mo> </mover> </math></EquationSource> </InlineEquation>r inequalities for LR-<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_514_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\((h_{1},h_{2})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>h</mi> <mn>2</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-convex interval-valued functions by means of pseudo-order relation (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40065_2025_514_Article_IEq5.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(\le _{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mo>≤</mo> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>). The results of this paper generalize previously known results and lay a preliminary foundation for the further study on interval post-quantum integral inequalities. Useful examples are provided to verify the validity of the theory established in this research.</p>

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Post-quantum Hermite–Hadamard type inequalities for LR-\((h_{1},h_{2})\)-convex interval-valued functions

  • 期刊论文

  • 发表日期：

    2025年5月10日

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  • Li Zhang,
  • Run Xu

摘要

The purpose of this study is to introduce new (p, q)-Hermite–Hadamard and (p, q)-Hermite–Hadamard–Fej \(\acute{e}\) e ´ r inequalities for LR- \((h_{1},h_{2})\) ( h 1 , h 2 ) -convex interval-valued functions by means of pseudo-order relation ( \(\le _{p}\) ≤ p ). The results of this paper generalize previously known results and lay a preliminary foundation for the further study on interval post-quantum integral inequalities. Useful examples are provided to verify the validity of the theory established in this research.