ANALYSIS OF NEWTON AND HERMITE–HADAMARD-TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITIES ON FRACTAL SETS USING GENERALIZED PRE-INVEXITY

Hui-Yan Cheng (), Ibrahim Mekawy (), Juan Wang (), Humera Batool and Muhammad Imran Qureshi ()
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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

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-15

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.

Keywords: Pre-Invex Functions; Newton-Type Inequality; Hermite–Hadamard Inequality; Local Fractional Integrals; Fractal Sets; Fractal Dimension (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401036

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