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Symmetrical Hermite–Hadamard type inequalities stemming from multiplicative fractional integrals

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  • Peng, Yu
  • Özcan, Serap
  • Du, Tingsong

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.

Suggested Citation

  • Peng, Yu & Özcan, Serap & Du, Tingsong, 2024. "Symmetrical Hermite–Hadamard type inequalities stemming from multiplicative fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924005125
    DOI: 10.1016/j.chaos.2024.114960
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    References listed on IDEAS

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    1. Butt, Saad Ihsan & Yousaf, Saba & Akdemir, Ahmet Ocak & Dokuyucu, Mustafa Ali, 2021. "New Hadamard-type integral inequalities via a general form of fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Xia Wu & JinRong Wang & Jialu Zhang, 2019. "Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel," Mathematics, MDPI, vol. 7(9), pages 1-12, September.
    3. Du, Tingsong & Zhou, Taichun, 2022. "On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex mappings," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    4. Wenbing Sun, 2021. "Hermite–Hadamard Type Local Fractional Integral Inequalities With Mittag-Leffler Kernel For Generalized Preinvex Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-13, December.
    5. Wenbing Sun & Haiyang Wan, 2023. "Hermite–Hadamard-Type Inequalities Involving Several Kinds Of Fractional Calculus For Harmonically Convex Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(09), pages 1-16.
    6. Set, Erhan & Butt, Saad Ihsan & Akdemir, Ahmet Ocak & Karaoǧlan, Ali & Abdeljawad, Thabet, 2021. "New integral inequalities for differentiable convex functions via Atangana-Baleanu fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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