# INEQUALITIES FOR CHORD POWER INTEGRALS

• Xiong, Ge (DEPARTMENT OF MATHEMATICS SHANGHAI UNIVERSITY) ;
• Song, Xiaogang (DEPARTMENT OF MATHEMATICS SHANGHAI UNIVERSITY)
• Published : 2008.03.31

#### Abstract

For convex bodies, chord power integrals were introduced and studied in several papers (see [3], [6], [14], [15], etc.). The aim of this article is to study them further, that is, we establish the Brunn-Minkowski-type inequalities and get the upper bound for chord power integrals of convex bodies. Finally, we get the famous Zhang projection inequality as a corollary. Here, it is deserved to mention that we make use of a completely distinct method, that is using the theory of inclusion measure, to establish the inequality.

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#### Cited by

1. CHORD POWER INTEGRALS OF SIMPLICES vol.02, pp.04, 2009, https://doi.org/10.1142/S1793557109000479
2. Random chord distributions and containment functions vol.58, 2014, https://doi.org/10.1016/j.aam.2014.05.003
3. Some inequalities for chord power integrals of parallelotopes vol.181, pp.4, 2016, https://doi.org/10.1007/s00605-016-0888-y