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<p>This article establishes a novel equality for twice-differentiable functions with convex absolute values in their second derivatives. This equality is used to establish Euler–Maclaurin-type inequalities through Riemann–Liouville fractional integrals. By utilizing convexity, the power mean inequality, and the Hölder inequality, several significant fractional inequalities can be derived. Moreover, the recently derived inequalities are not only grounded in theory but are also accompanied by concrete instances to further solidify their validity.</p>

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Fractional Euler–Maclaurin-type inequalities for twice-differentiable functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月28日

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  • Asia Shehzadi,
  • Hüseyin Budak,
  • Wali Haider,
  • Fatih Hezenci,
  • Haibo Chen

摘要

This article establishes a novel equality for twice-differentiable functions with convex absolute values in their second derivatives. This equality is used to establish Euler–Maclaurin-type inequalities through Riemann–Liouville fractional integrals. By utilizing convexity, the power mean inequality, and the Hölder inequality, several significant fractional inequalities can be derived. Moreover, the recently derived inequalities are not only grounded in theory but are also accompanied by concrete instances to further solidify their validity.