Symmetrical Hermite–Hadamard type inequalities stemming from multiplicative fractional integrals

Yu Peng, Serap Özcan and Tingsong Du

Chaos, Solitons & Fractals, 2024, vol. 183, issue C

Abstract: We firstly study ∗integrability and commutativity for multiplicative fractional integrals with exponential kernels, proposed by Peng et al. (2022). Secondly, making use of such operators, we present a symmetrical multiplicative fractional integrals identity. Based on it, and the fact that the function T∗ is multiplicatively convex or the function (lnT∗)θ is convex for θ>1, especially pondering the case of 0<θ≤1, we establish the symmetrical Hermite–Hadamard type inequalities for multiplicative convexity. We also give some applications in special means under multiplicative calculus.

Keywords: Hermite–Hadamard’s inequality; Multiplicative Riemann–Liouville fractional integrals; Multiplicative differentiable functions (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924005125

DOI: 10.1016/j.chaos.2024.114960

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