In this paper, we investigate some new generalizations and refinements for Holder’s inequality and it’s reverse on time scales through the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. Our results as special cases extend some integral dynamic inequalities and Qi’s inequalities achieved on time scales and also include some integral disparities as particular cases when T=R.

中文翻译：

---

更多关于 Hölder 不等式及其通过 Diamond-Alpha 积分求逆

在本文中，我们研究了 Holder 不等式的一些新的推广和改进，它通过菱形-α 动态积分在时间尺度上反转，该积分定义为 delta 和 nabla 积分的线性组合，用于涉及对称性的各种问题. 我们将一些对称不等式发展到一般时间尺度。我们作为特殊情况的结果扩展了一些积分动态不等式和时间尺度上实现的 Qi 不等式，还包括一些积分差异作为 T=R 时的特殊情况。