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Hermite-Hadamard inequalities for quantum integrals: A unified approach

Author

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  • Cardoso, J.L.
  • Shehata, Enas M.

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.

Suggested Citation

  • Cardoso, J.L. & Shehata, Enas M., 2024. "Hermite-Hadamard inequalities for quantum integrals: A unified approach," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    • Handle: RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005143
    DOI: 10.1016/j.amc.2023.128345
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    References listed on IDEAS

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    1. M. H. Annaby & A. E. Hamza & K. A. Aldwoah, 2012. "Hahn Difference Operator and Associated Jackson–Nörlund Integrals," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 133-153, July.
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