In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.

中文翻译：

---

通过广义分数积分对调和凸函数的 Hermite-Hadamard 不等式进行扩展

在论文中，作者通过广义分数积分为调和凸函数建立了一些新的 Hermite-Hadamard 型不等式。此外，作者通过广义分数积分证明了调和凸函数的 Hermite-Hadamard 不等式的扩展，而不使用函数的调和凸性。此处提供的结果是对调和凸函数的现有结果的改进。