Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2008.12.08
  • Published : 2010.09.01
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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.

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References

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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