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<p>This paper presents enhanced parameterized quantum Hermite-Hadamard type integral inequalities for functions whose third right and left <i>q</i>-derivatives in absolute value are strongly convex functions. We obtain new bounds using H<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2024_1123_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ddot{o}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>o</mi> <mo>¨</mo> </mover> </math></EquationSource> </InlineEquation>lder’s and power mean inequalities as primary tools. Also, we derive new quantum estimates for <i>q</i>-trapezoidal and <i>q</i>-midpoints type inequalities in specific scenarios, which we illustrate with examples. These outcomes possess the potential for practical applications in optimizing various economic problems.</p>

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Quantum analogue of Hermite-Hadamard type inequalities for strongly convex functions

  • 期刊论文

  • 发表日期：

    2024年12月31日

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  • Shashi Kant Mishra,
  • Ravina Sharma,
  • Jaya Bisht

摘要

This paper presents enhanced parameterized quantum Hermite-Hadamard type integral inequalities for functions whose third right and left q-derivatives in absolute value are strongly convex functions. We obtain new bounds using H \(\ddot{o}\) o ¨ lder’s and power mean inequalities as primary tools. Also, we derive new quantum estimates for q-trapezoidal and q-midpoints type inequalities in specific scenarios, which we illustrate with examples. These outcomes possess the potential for practical applications in optimizing various economic problems.