NEW FRACTIONAL INTEGRAL INEQUALITIES FOR LR-â„ -PREINVEX INTERVAL-VALUED FUNCTIONS

Yun Tan () and Dafang Zhao
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Yun Tan: 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

FRACTALS (fractals), 2024, vol. 32, issue 05, 1-14

Abstract: Based on the pseudo-order relation, we introduce the concept of left and right ℠-preinvex interval-valued functions (LR-℠-PIVFs). Further, we establish the Hermite–Hadamard and Hermite–Hadamard–Fejér-type estimates for LR-℠-PIVFs using generalized fractional integrals. Finally, an example of interval-valued fractional integrals is provided to illustrate the validity of the results derived herein. Our results not only extend some existing inequalities for Hadamard, Riemann–Liouville, and Katugampola fractional integrals, but also provide new insights for future research on generalized convexity and IVFs, among others.

Keywords: Hermite–Hadamard Inequalities; Hermite–Hadamard–Fejér Inequalities; LR-℠-Preinvex Functions; Interval-Valued Functions; Fractional Integrals (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X2450083X

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