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<p>This paper develops a novel Milne inequality for third-differentiable and <i>h</i>-convex functions using Riemann integrals. Furthermore, new Milne inequalities are proposed utilizing a summation parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2024_1984_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>p</mi> <mo>≥</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$p\geq 1$</EquationSource> </InlineEquation> for <i>s</i>-convexity, convexity, and <i>P</i>-functions class. We examine cases when the third derivative functions are also bounded and Lipschitzian.</p>

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Milne-type inequalities for third differentiable and h-convex functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月7日

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  • Bouharket Benaissa,
  • Hüseyin Budak

摘要

This paper develops a novel Milne inequality for third-differentiable and h-convex functions using Riemann integrals. Furthermore, new Milne inequalities are proposed utilizing a summation parameter p ≥ 1 $p\geq 1$ for s-convexity, convexity, and P-functions class. We examine cases when the third derivative functions are also bounded and Lipschitzian.