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Abstract <p>In the present study, some types of the Hermite–Hadamard (H–H) fractional integral inequality, with Riemann–Liouville fractional integral for functions whose absolute values of the first derivatives of positive real powers (AVFDPRPs) are <i>s</i>-geometrically convex, have been discussed. It has been also concluded for geometrically convex. As an application, by using special mean of real numbers, H–H inequalities with ordinary integral have been generalized for functions whose AVFDPRPs are geometrically convex or <i>s</i>-geometrically convex.</p>

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New Hermite–Hadamard Fractional Integral Inequalities for s-Geometry. Convex Functions

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • H. Talebi,
  • A. Neamaty

摘要

Abstract

In the present study, some types of the Hermite–Hadamard (H–H) fractional integral inequality, with Riemann–Liouville fractional integral for functions whose absolute values of the first derivatives of positive real powers (AVFDPRPs) are s-geometrically convex, have been discussed. It has been also concluded for geometrically convex. As an application, by using special mean of real numbers, H–H inequalities with ordinary integral have been generalized for functions whose AVFDPRPs are geometrically convex or s-geometrically convex.