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<p>In this paper, we first introduced two time scales based on the interval [<i>a</i>,&#xa0;<i>b</i>] and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1106_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\( \mathbb {Z} \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Z</mi> </math></EquationSource> </InlineEquation>. Then, by using one of these time scale and substitutions rules, we prove a new version of discrete Hermite-Hadamard inequality for discrete convex functions. Moreover, we investigate the fractional version of this inequality involving fractional delta and nabla sums.</p>

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New versions of Hermite–Hadamard inequalities on Discrete Time Scales

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • Hüseyin Budak

摘要

In this paper, we first introduced two time scales based on the interval [a, b] and \( \mathbb {Z} \) Z . Then, by using one of these time scale and substitutions rules, we prove a new version of discrete Hermite-Hadamard inequality for discrete convex functions. Moreover, we investigate the fractional version of this inequality involving fractional delta and nabla sums.