In this paper, some new inequalities of the Hermite–Hadamard type for the classes of functions whose derivatives’ absolute values are m-convex and $( \alpha , m) $-convex are obtained. The results obtained in this work extend and improve the corresponding ones in the literature. Some applications to special means of real numbers are also given.

中文翻译：

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m-凸和\（（（\ alpha，m）\）-凸函数的Hermite–Hadamard型不等式

在本文中，获得了其函数的导数的绝对值为m-凸和$（\ alpha，m）$-凸的函数类的Hermite-Hadamard类型的一些新不等式。在这项工作中获得的结果扩展并改进了文献中的相应结果。还给出了一些特殊的实数方法应用。