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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, Hindawi, vol. 2025, pages 1-20, December.
    • Handle: RePEc:hin:jjmath:1669917
    DOI: 10.1155/jom/1669917
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