Hermite-Hadamard inequalities for quantum integrals: A unified approach

J.L. Cardoso and Enas M. Shehata

Applied Mathematics and Computation, 2024, vol. 463, issue C

Abstract: Let s0 be a fixed point of a strictly increasing continuous function β. Hamza et al. introduced the quantum operator Dβ[g](θ):=g(β(θ))−g(θ)β(θ)−θ, θ≠s0 and Dβ[g](s0):=g′(s0) if θ=s0. For specific choices of the function β one obtains the known Jackson q-operator Dq as well as the Hahn quantum operator Dq,ω. Regarding its inverse operator, the β-integral, we establish the corresponding β-Hermite-Hadamard inequalities. Among others, we also obtain the Hermite-Hadamard type inequalities for the Jackson q-integral, the Nörlund integral and for the Jackson-Thomae (or Jackson-Nörlund) q,ω-integral.

Keywords: Hermite-Hadamard inequalities; Convex function; β-Hermite-Hadamard inequalities; General quantum difference operator; β-derivative; β-integral (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005143

DOI: 10.1016/j.amc.2023.128345

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