# MIXED BRIGHTNESS-INTEGRALS OF CONVEX BODIES

• Li, Ni (COLLEGE OF MATHEMATICS AND COMPUTER SCIENCE CHONGQING NORMAL UNIVERSITY) ;
• Zhu, Baocheng (COLLEGE OF MATHEMATICS AND COMPUTER SCIENCE CHONGQING NORMAL UNIVERSITY)
• Published : 2010.09.01
• 105 7

#### Abstract

The mixed width-integrals of convex bodies are defined by E. Lutwak. In this paper, the mixed brightness-integrals of convex bodies are defined. An inequality is established for the mixed brightness-integrals analogous to the Fenchel-Aleksandrov inequality for the mixed volumes. An isoperimetric inequality (involving the mixed brightness-integrals) is presented which generalizes an inequality recently obtained by Chakerian and Heil. Strengthened version of this general inequality is obtained by introducing indexed mixed brightness-integrals.

#### Keywords

convex bodies;mixed projection bodies;brightness;mixed brightness;mixed brightness-integrals;Fenchel-Aleksandrov inequality

#### Acknowledgement

Supported by : Nature Science Foundation of China

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#### Cited by

1. Inequalities for mixed width-integrals vol.21, pp.3, 2016, https://doi.org/10.1007/s11859-016-1157-6
2. The Brunn-Minkowski type inequalities for mixed brightness-integrals vol.19, pp.4, 2014, https://doi.org/10.1007/s11859-014-1013-5
3. General L p $L_{p}$ -mixed-brightness integrals vol.2015, pp.1, 2015, https://doi.org/10.1186/s13660-015-0708-2