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<p>The main goal of this paper is a study of more precise power mean inequalities based on a superquadraticity. Our main results lean on a strengthened form of the Jensen inequality that holds for a class of non-negative superquadratic functions. In addition, even more accurate class of power mean inequalities has been established by using the invariance of a variance with respect to the translation. Finally, some generalized power mean inequalities are obtained throughout extension of a concept of superquadraticity, namely so called <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13398_2025_1790_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-superquadraticity.</p>

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Strengthened power mean inequalities based on superquadraticity

  • 期刊论文

  • 发表日期：

    2025年9月22日

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  • Marija Bošnjak,
  • Mario Krnić

摘要

The main goal of this paper is a study of more precise power mean inequalities based on a superquadraticity. Our main results lean on a strengthened form of the Jensen inequality that holds for a class of non-negative superquadratic functions. In addition, even more accurate class of power mean inequalities has been established by using the invariance of a variance with respect to the translation. Finally, some generalized power mean inequalities are obtained throughout extension of a concept of superquadraticity, namely so called \(\gamma \) γ -superquadraticity.