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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. 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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