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Fejér–Hermite–Hadamard type inequalities involving generalized h-convexity on fractal sets and their applications

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  • Luo, Chunyan
  • Wang, Hao
  • Du, Tingsong

Abstract

This article aims to investigate certain inequalities for generalized h-convexity on fractal sets Rα, which are related to the famous Fejér–Hermite–Hadamard inequality. For this purpose, two identities for local differentiable mappings are established, based on which we provide certain estimates for the difference between the left and middle part as well as that of the middle and right part in the Fejér–Hermite–Hadamard inequality. Furthermore, we present five examples to illustrate the obtained results. As applications related to local fractional integrals, we construct several inequalities for random variables, cumulative distribution functions and numerical integrations.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919305041
    DOI: 10.1016/j.chaos.2019.109547
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    1. Rostamian Delavar, M. & Dragomir, S.S., 2019. "Weighted trapezoidal inequalities related to the area balance of a function with applications," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 5-14.
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    4. Du, Tingsong & Li, Yujiao & Yang, Zhiqiao, 2017. "A generalization of Simpson’s inequality via differentiable mapping using extended (s, m)-convex functions," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 358-369.
    5. Hwang, Dah-Yan, 2014. "Some inequalities for differentiable convex mapping with application to weighted midpoint formula and higher moments of random variables," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 68-75.
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    Cited by:

    1. Meftah, B. & Souahi, A. & Merad, M., 2022. "Some local fractional Maclaurin type inequalities for generalized convex functions and their applications," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Asfand Fahad & Ayesha & Yuanheng Wang & Saad Ihsaan Butt, 2023. "Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA- h -Convex Functions and Its Subclasses with Applications," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    3. Du, Tingsong & Yuan, Xiaoman, 2023. "On the parameterized fractal integral inequalities and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Cheng, Qingjin & Luo, Chunyan, 2022. "Estimation of the parameterized integral inequalities involving generalized p-convex mappings on fractal sets and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    5. Yu, Shuhong & Zhou, Yunxiu & Du, Tingsong, 2022. "Certain midpoint-type integral inequalities involving twice differentiable generalized convex mappings and applications in fractal domain," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. 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).
    7. Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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