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A generalization of Simpson’s inequality via differentiable mapping using extended (s, m)-convex functions

Author

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  • Du, Tingsong
  • Li, Yujiao
  • Yang, Zhiqiao

Abstract

The authors deduce a differentiable mapping integral identity with two parameters. Using this integral identity, this paper establishes new inequalities of Simpson type for extended (s, m)-convex functions under certain conditions. This contributes to new better estimates than the earlier results. Finally, these inequalities are applied to special means.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:293:y:2017:i:c:p:358-369
    DOI: 10.1016/j.amc.2016.08.045
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    Cited by:

    1. Hüseyin Budak & Fatih Hezenci & Hasan Kara & Mehmet Zeki Sarikaya, 2023. "Bounds for the Error in Approximating a Fractional Integral by Simpson’s Rule," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    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. Muhammad Aamir Ali & Zhiyue Zhang & Michal Fečkan, 2022. "On Some Error Bounds for Milne’s Formula in Fractional Calculus," Mathematics, MDPI, vol. 11(1), pages 1-11, December.

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