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In this paper, we introduce the Lp$L_{p}$-mixed mean zonoid of convex bodies K and L, and we prove some important properties for the Lp$L_{p}$-mixed mean zonoid, such as monotonicity, GL(n)$\operatorname{GL}(n)$ covariance, and so on. We also establish new affine isoperimetric inequalities for the Lp$L_{p}$-mixed mean zonoid.

Affine inequalities for L p $L_{p}$ -mixed mean zonoids