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The mixed brightness-integrals were defined by Li and Zhu. In this paper, we first establish two Brunn-Minkowski inequalities of the mixed brightness-integrals based on the Blaschke sum and Minkowski sum of convex bodies. Further, we also obtain the Beckenbach-Dresher type inequalities of the mixed brightness-integrals combining the harmonic Blaschke sum and the harmonic radial sum of star bodies.
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