Abstract In the paper, the concept of Lp -dual three-mixed quermassintegrals is introduced. The formula for the Lp -dual three-mixed quermassintegrals with respect to the p-radial addition is proved. Inequalities of Lp -Minkowski, and Brunn-Minkowski type for the Lp -dual three-mixed quermassintegrals are established. The new Lp -Minkowski inequality is obtained that generalize a family of Minkowski type inequalities. The Lp -Brunn-Minkowski inequality is used to obtain a series of Brunn-Minkowski type inequalities.

中文翻译：

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Lp - 双三混合 quermassintegrals

摘要 介绍了Lp-对偶三混合quermassintegrals的概念。证明了Lp-对偶三混合quermassintegrals关于p-径向加法的公式。建立了Lp-对偶三混合quermassintegrals的Lp-Minkowski和Brunn-Minkowski型不等式。得到了新的 Lp -Minkowski 不等式，它推广了一系列 Minkowski 型不等式。Lp -Brunn-Minkowski 不等式用于获得一系列 Brunn-Minkowski 型不等式。