Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (6): 1049-1057.

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Some Properties and Inequalities for Chord-Integrals of Star Bodies

Chunna Zeng1(),Ran Li2(),Baocheng Zhu3,*()   

  1. 1 School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
    2 SDFZ Experimental School, Shandong Heze 404100
    3 Department of Mathematics, Hubei University for Nationalities, Hubei Enshi 445000
  • Received:2017-09-20 Online:2018-12-26 Published:2018-12-27
  • Contact: Baocheng Zhu E-mail:zengchn@163.com;lizhunran@163.com;zhubaocheng814@163.com
  • Supported by:
    Supported by the NSFC(11501185);Supported by the NSFC(11801048);the Chongqing Basic Science and Frontier Technology Research Project(cstc2017jcyjAX0022);the Venture & Innovation Support Program for Chongqing Overseas Returnees(cx2018034)

Abstract:

In this paper, we obtain some limit properties of chord-integrals in $\mathbb{R}$n, and establish some inequalities for chord-integrals of star bodies, including the inequalities between chord-integrals and dual quermass-integrals, the dual Blaschke-Santaló inequality and so on.

Key words: Convex bodies, Star bodies, Width-integrals, Chord-integrals

CLC Number: 

  • O186.5
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