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Analysis Of Newton And Hermite–Hadamard-Type Local Fractional Integral Inequalities On Fractal Sets Using Generalized Pre-Invexity

Author

Listed:
  • HUI-YAN CHENG

    (Department of Basic Education, Zhengzhou Technology and Business University, Zhengzhou, P. R. China)

  • IBRAHIM MEKAWY

    (Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia)

  • JUAN WANG

    (Faculty of Engineering, Anhui Sanlian University, Hefei, P. R. China)

  • HUMERA BATOOL

    (School of Mathematics, Liaocheng University, Liaocheng 252000, P. R. China)

  • MUHAMMAD IMRAN QURESHI

    (Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari, Pakistan)

Abstract

Motivated by the growing interest in fractional analysis in medicine, we established some exciting results on fractal sets and their complex generalized versions that can help improve existing results. In this work, inspired by two Generalized Local Fractional Integrals (GLFIs), Hermite–Hadamard Inequality (HHI) for extended â… -pre-invex mappings (â… -PMs) is established, connected to a Modified Mittag-Leffler Kernel (MMLK). This study aims to analyze especially Parametrized Integral Inequalities (PIIs) related to 1–4-point Newton–Cotes formulae (NCFs), which can be applied to a differentiable (via local fractional derivative) and generalized â… -PMs. We use a unique integral local fractional identity and modify various integral inequalities related to generalized â… -PMs. Finally, we show 3D plots using two fascinating examples.

Suggested Citation

  • Hui-Yan Cheng & Ibrahim Mekawy & Juan Wang & Humera Batool & Muhammad Imran Qureshi, 2025. "Analysis Of Newton And Hermite–Hadamard-Type Local Fractional Integral Inequalities On Fractal Sets Using Generalized Pre-Invexity," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-15.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:04:n:s0218348x25401036
    DOI: 10.1142/S0218348X25401036
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