In this manuscript, we introduce the concept of geometric trigonometrically convex functions. We obtain some refinements of the Hermite–Hadamard inequality for functions whose first derivative in absolute value is geometric trigonometrically convex. In addition, it has been proved that the results obtained with Hölder–İşcan and improved power‐mean integral inequalities give a better approach than Hölder and power‐mean inequalities.

中文翻译：

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几何三角凸和更好的近似

在本手稿中，我们介绍了几何三角凸函数的概念。对于函数的绝对值的一阶导数是几何三角凸的函数，我们获得了Hermite-Hadamard不等式的一些改进。此外，已经证明，使用Hölder–İşcan获得的结果和改进的幂均值积分不等式比Hölder和幂均值不等式提供了更好的方法。