In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

中文翻译：

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广义分数积分的区间值近似h-凸函数的Hermite-Hadamard型不等式

在本文中，我们根据给定的函数给出了区间值凸函数的新定义，称为“区间值近似h凸函数”。通过使用广义分数积分，我们为新定义的函数类建立了Hermite–Hadamard类型的不等式。我们的新不等式是先前获得的结果的扩展，例如（DF Zhao等人，J.Inequal.Appl.2018（1）：302，2018和H.B​​udak等人，Proc.Am.Math.Soc。，2019 ）。我们还从主要结果中讨论了一些特殊情况。