In this study, using power‐mean inequality and improved power‐mean integral inequality better approach than power‐mean inequality and an identity for differentiable functions, we get inequalities for functions whose derivatives in absolute value at certain power are convex. Numerically, it is shown that improved power‐mean integral inequality gives better approach than power‐mean inequality. Some applications to special means of real numbers and some error estimates for the midpoint formula are also given.

中文翻译：

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关于使用改进的幂均值积分不等式来完善某些积分不等式

在这项研究中，通过使用幂均值不等式和改进的幂均值积分不等式比幂均值不等式更好的方法以及可微函数的恒等式，我们得到了在一定幂次下的绝对值导数是凸的函数不等式。从数字上可以看出，改进的幂均值积分不等式比幂均值不等式提供了更好的方法。还给出了对实数的特殊方法的一些应用，以及对中点公式的一些误差估计。