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Generalized Fejér–Hermite–Hadamard type via generalized (h−m)-convexity on fractal sets and applications

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  • Almutairi, Ohud
  • Kiliçman, Adem

Abstract

In this article, we define a new class of convexity called generalized (h−m)-convexity, which generalizes h-convexity and m-convexity on fractal set Rα(0<α≤1). Some properties of this new class are discussed. Using local fractional integrals and generalized (h−m)-convexity, we generalized Hermite–Hadamard (H–H) and Fejér–Hermite–Hadamard (Fejér–H–H) types inequalities. We also obtained a new result of the Fejér–H–H type for the function whose derivative in absolute value is the generalized (h−m)-convexity on fractal sets. As applications, we studied some new inequalities for random variables, numerical integrations and generalized to special means.

Suggested Citation

  • Almutairi, Ohud & Kiliçman, Adem, 2021. "Generalized Fejér–Hermite–Hadamard type via generalized (h−m)-convexity on fractal sets and applications," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921002927
    DOI: 10.1016/j.chaos.2021.110938
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    References listed on IDEAS

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    1. Huixia Mo & Xin Sui, 2014. "Generalized -Convex Functions on Fractal Sets," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, July.
    2. Luo, Chunyan & Wang, Hao & Du, Tingsong, 2020. "Fejér–Hermite–Hadamard type inequalities involving generalized h-convexity on fractal sets and their applications," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Huixia Mo & Xin Sui & Dongyan Yu, 2014. "Generalized Convex Functions on Fractal Sets and Two Related Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, June.
    4. Sarikaya, Mehmet Zeki & Tunc, Tuba & Budak, Hüseyin, 2016. "On generalized some integral inequalities for local fractional integrals," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 316-323.
    5. Chahn Yong Jung & Ghulam Farid & Sidra Bibi & Kottakkaran Sooppy Nisar & Shin Min Kang & Nan-Jing Huang, 2020. "Hadamard-Type k-Fractional Integral Inequalities for Exponentially α,h−m-Convex Functions," Journal of Mathematics, Hindawi, vol. 2020, pages 1-17, October.
    6. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    7. Danane, Jaouad & Allali, Karam & Hammouch, Zakia, 2020. "Mathematical analysis of a fractional differential model of HBV infection with antibody immune response," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    8. 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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    1. Du, Tingsong & Yuan, Xiaoman, 2023. "On the parameterized fractal integral inequalities and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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