In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

中文翻译：

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量子可微凸函数的某些量子积分不等式的新推广。

在本文中，我们提供了一个新的量子积分恒等式，然后将结果用于获得量子积分的Hermite-Hadamard不等式的一些新估计。本文介绍的结果是有关Hermite-Hadamard不等式文献中可比结果的概括。作为我们主要结果的特例，获得了一些不等式，例如中点类积分不等式，Simpson类积分不等式，平均中点-梯形积分不等式和梯形类积分不等式。