Some new Hermite-Hadamard type inequalities for generalized harmonically convex functions involving local fractional integrals

Wenbing Sun; Rui Xu; Wenbing Sun; Rui Xu

doi:10.3934/math.2021620

AIMS Mathematics

2021, Volume 6, Issue 10: 10679-10695. doi: 10.3934/math.2021620

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Research article

Some new Hermite-Hadamard type inequalities for generalized harmonically convex functions involving local fractional integrals

Wenbing Sun ,
Rui Xu ^,

School of Science, Shaoyang University, Shaoyang 422000, China

Received: 29 May 2021 Accepted: 20 July 2021 Published: 23 July 2021
MSC : 26D15, 26A51, 26D10

In this paper, we establish a new integral identity involving local fractional integral on Yang's fractal sets. Using this integral identity, some new generalized Hermite-Hadamard type inequalities whose function is monotonically increasing and generalized harmonically convex are obtained. Finally, we construct some generalized special means to explain the applications of these inequalities.
- Hermite-Hadamard type inequality,
- generalized harmonically convex function,
- Yang's fractal sets,
- local fractional integral
Citation: Wenbing Sun, Rui Xu. Some new Hermite-Hadamard type inequalities for generalized harmonically convex functions involving local fractional integrals[J]. AIMS Mathematics, 2021, 6(10): 10679-10695. doi: 10.3934/math.2021620

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Abstract

In this paper, we establish a new integral identity involving local fractional integral on Yang's fractal sets. Using this integral identity, some new generalized Hermite-Hadamard type inequalities whose function is monotonically increasing and generalized harmonically convex are obtained. Finally, we construct some generalized special means to explain the applications of these inequalities.

References

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