FRACTIONAL QUANTUM HERMITE–HADAMARD-TYPE INEQUALITIES FOR INTERVAL-VALUED FUNCTIONS

Haiyang Cheng (), Dafang Zhao and Guohui Zhao
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Haiyang Cheng: School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, P. R. China
Dafang Zhao: School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, P. R. China†National Cryosphere Desert Data Center, Lanzhou 730000, P. R. China
Guohui Zhao: ��National Cryosphere Desert Data Center, Lanzhou 730000, P. R. China‡Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou 73000, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 09, 1-13

Abstract: Based on the q-shifting operator, we introduce the concept of Riemann–Liouville fractional quantum integration for interval-valued functions (IVFs), and establish new Riemann–Liouville fractional q-Hermite–Hadamard (q-HH) and q-HH-Fejér inequalities for left and right h-convex IVFs (LR-℠-convex-IVFs). The findings obtained generalize known results in the literature and serve as a foundation for future studies in inequalities for interval-valued functions and fractional quantum calculus. The results are illustrated with examples.

Keywords: Fractional Quantum Integration; Hermite–Hadamard Inequalities; Order Relations; Convexity; Interval-Valued Functions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23501049

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