In this research, we introduce the notions of $(p,q)$ -derivative and integral for interval-valued functions and discuss their fundamental properties. After that, we prove some new inequalities of Hermite–Hadamard type for interval-valued convex functions employing the newly defined integral and derivative. Moreover, we find the estimates for the newly proved inequalities of Hermite–Hadamard type. It is also shown that the results proved in this study are the generalization of some already proved research in the field of Hermite–Hadamard inequalities.

中文翻译：

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区间值凸函数的量子后Hermite-Hadamard型不等式

在这项研究中，我们介绍了区间值函数$（p，q）$-导数和积分的概念，并讨论了它们的基本性质。之后，我们证明了使用新定义的积分和导数的区间值凸函数的Hermite-Hadamard类型的一些新的不等式。此外，我们找到了Hermite–Hadamard类型新证明的不等式的估计。还表明，本研究证明的结果是对Hermite-Hadamard不等式领域中一些已经证明的研究的概括。