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<p>In this paper, firstly we introduced <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2024_2605_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-geometric mean and a new class of convex functions called <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2024_2605_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-<i>GA</i>-convex functions. After that, we established some new inequalities involving Hermite-Hadamard type inequality and Jensen-Mercer type inequality, for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2024_2605_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-<i>GA</i>-convex functions. Finally, we give some applications of the obtained results.</p>

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A Generalization of GA-convex Functions and Applications

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Hasan Barsam,
  • Yamin Sayyari

摘要

In this paper, firstly we introduced \(\delta \) δ -geometric mean and a new class of convex functions called \(\delta \) δ -GA-convex functions. After that, we established some new inequalities involving Hermite-Hadamard type inequality and Jensen-Mercer type inequality, for \(\delta \) δ -GA-convex functions. Finally, we give some applications of the obtained results.