EXPLORING FRACTIONAL HERMITE–HADAMARD INCLUSIONS IN UP–DOWN FUZZY MECHANISM ASSOCIATED WITH MULTIPLE HARMONIC CONVEXITIES

Jie Li (), Muhammad Bilal Riaz, El-Sayed M. Sherif (), Ahsan Fareed Shah () and Adil Jhangeer ()
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Jie Li: Faculty of Mathematics and Statistics, Suzhou University, Suzhou, Anhui 234000, P. R. China
Muhammad Bilal Riaz: IT4Innovations, VSB — Technical, University of Ostrava, Ostrava, Czech Republic3Applied Science Research Center, Applied Science Private University, Amman, Jordan
El-Sayed M. Sherif: Mechanical Engineering Department, College of Engineering, King Saud University, Al-Riyadh, Saudi Arabia
Ahsan Fareed Shah: Department of Mathematics, University of Okara, Okara, Pakistan
Adil Jhangeer: IT4Innovations, VSB — Technical, University of Ostrava, Ostrava, Czech Republic

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-16

Abstract: Our study explores a new concept: merging fuzzy-valued convex mappings that collaborate with the up–down fuzzy inclusion mechanism. This latest version of convexity links to various other convexities as well, which have been previously presented in the literature. So, applying this idea benefits us with several modifications of Fuzzy Fractional Hermite–Hadamard (ℋ−ℋ) and Fejér inclusions. To examine the importance and accuracy of our results, we provide graphical insights by considering simple, understandable examples. These findings, which contribute to a greater understanding of fuzzy fractional integrals of the harmonical mean type, are new and unique.

Keywords: Harmonically γ-Convex Fuzzy-Number-Valued Functions; Up–Down Inclusion Relation; Fuzzy Aumann Integral; Fractional Integrals; Hermite Hadamard–Fejér-Type Inequality (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401589

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