HERMITE–HADAMARD TYPE INEQUALITIES FOR ℠-CONVEX FUNCTION VIA FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL

Haiyang Cheng (), Dafang Zhao and Mehmet Zeki Sarikaya ()
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Haiyang Cheng: Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, P. R. China
Dafang Zhao: Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, P. R. China
Mehmet Zeki Sarikaya: ��Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey

FRACTALS (fractals), 2024, vol. 32, issue 02, 1-15

Abstract: Fractional q-calculus is considered to be the fractional analogs of q-calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) q-integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving ℠-convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF q-integral. The results not only generalize existing findings in the literature but also lay a solid foundation for research on inequalities concerning FIVFs. Moreover, to verify our theoretical findings, numerical examples and imperative graphical illustrations are provided.

Keywords: Hermite–Hadamard Inequalities; ℠-Convexity; Fractional Integral; Quantum Integral; Fuzzy Interval-Valued Functions (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500427

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