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A Fractal Approach to Hermite–Hadamard Type Inequalities via Generalized Beta Function

Author

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  • Saad Ihsan Butt
  • Muhammad Mehtab
  • Youngsoo Seol

Abstract

The main aim of this manuscript is to explore the connection between fractal geometry and convexity, highlighting the mathematical appeal of fractals. Using the beta function, we introduce a new class of generalized Hermite–Hadamard (HH) type inequalities. This work adds meaningful results of new versions of fractal Hölder’s and Young’s inequalities. We establish some general conclusions that incorporate new results under study, considering the new concept. Another valuable contribution of the research is that two new auxiliary results are given. Trapezoidal and midpoint type inequalities are given. Special means and special function applications are also presented. We establish connections with our results and several well‐established findings in the literature.

Suggested Citation

  • Saad Ihsan Butt & Muhammad Mehtab & Youngsoo Seol, 2025. "A Fractal Approach to Hermite–Hadamard Type Inequalities via Generalized Beta Function," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:1669917
    DOI: 10.1155/jom/1669917
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    References listed on IDEAS

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    1. Sheng-Ping Yan & Hossein Jafari & Hassan Kamil Jassim, 2014. "Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    2. Saad Ihsan Butt & Dawood Khan & Youngsoo Seol, 2025. "Fractal perspective of superquadratic functions with generalized probability estimations," PLOS ONE, Public Library of Science, vol. 20(2), pages 1-24, February.
    3. Huixia Mo & Xin Sui & Dongyan Yu, 2014. "Generalized Convex Functions on Fractal Sets and Two Related Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, June.
    4. Yong Zhang & Wenbing Sun, 2024. "On General Local Fractional Integral Inequalities For Generalized H-Preinvex Functions On Yang’S Fractal Sets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-13.
    5. Huixia Mo & Xin Sui & Dongyan Yu, 2014. "Generalized Convex Functions on Fractal Sets and Two Related Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. Wenbing Sun, 2021. "Hermite–Hadamard Type Local Fractional Integral Inequalities With Mittag-Leffler Kernel For Generalized Preinvex Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-13, December.
    7. Sheng-Ping Yan & Hossein Jafari & Hassan Kamil Jassim, 2014. "Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-7, June.
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