The aim of this study is to introduce the notion of two-dimensional approximately harmonic $(p_{1},h_{1})$ - $(p_{2},h_{2})$ -convex functions. We show that the new class covers many new and known extensions of harmonic convex functions. We formulate several new refinements of Hermite–Hadamard like inequalities involving two-dimensional approximately harmonic $(p_{1},h_{1})$ - $(p_{2},h_{2})$ -convex functions. We discuss in detail the special cases that can be deduced from the main results of the paper.

中文翻译：

---

大约二维谐波\（（p_ {1}，h_ {1}）\） - \（（p_ {2}，h_ {2}）\）-凸函数和相关的积分不等式

这项研究的目的是介绍二维近似谐波$（p_ {1}，h_ {1}）$-$（p_ {2}，h_ {2}）$-凸函数的概念。我们证明新类涵盖了谐波凸函数的许多新的和已知的扩展。我们制定了Hermite–Hadamard的一些新改进，例如涉及包含二维近似谐波$（p_ {1}，h_ {1}）$-$（p_ {2}，h_ {2}）$-凸函数的不等式。我们将详细讨论可以从本文的主要结果中得出的特殊情况。