This paper is devoted to establishing some Hermite–Hadamard-type inequalities for interval-valued functions using the coordinated h-convexity, which is more general than classical convex functions. We also discuss the relationship between coordinated h-convexity and h-convexity. Furthermore, we introduce the concepts of minimum expansion and maximum contraction of interval sequences. Based on these two new concepts, we establish some new Hermite–Hadamard-type inequalities, which generalize some known results in the literature. Additionally, some examples are given to illustrate our results.

中文翻译：

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关于协调 h-凸区间值函数的 Hermite-Hadamard 型不等式

本文致力于使用比经典凸函数更通用的协调h凸性为区间值函数建立一些 Hermite-Hadamard 型不等式。我们还讨论了协调h -凸性和h -凸性之间的关系。此外，我们引入了区间序列的最小扩展和最大收缩的概念。基于这两个新概念，我们建立了一些新的 Hermite-Hadamard 型不等式，这些不等式概括了文献中的一些已知结果。此外，还给出了一些示例来说明我们的结果。