In the paper, we generalize the well-known Bellman’s and Popoviciu’s inequalities, and get new Bellman’s and Popoviciu’s type inequalities. These new results provide new estimates on inequalities of these type. As application, we establish a Minkowski inequality, which in special case yields the well-known dual Minkowski inequality for volumes difference.

中文翻译：

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Popoviciu 和 Bellman 不等式的推广

在本文中，我们对著名的Bellman 和Popoviciu 不等式进行了推广，得到了新的Bellman 和Popoviciu 类型不等式。这些新结果提供了对此类不平等的新估计。作为应用，我们建立了一个 Minkowski 不等式，它在特殊情况下产生了众所周知的体积差异的对偶 Minkowski 不等式。