• Title, Summary, Keyword: chord power integrals

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INEQUALITIES FOR CHORD POWER INTEGRALS

  • Xiong, Ge;Song, Xiaogang
    • Journal of the Korean Mathematical Society
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    • v.45 no.2
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    • pp.587-596
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    • 2008
  • 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.

MIXED CHORD-INTEGRALS OF STAR BODIES

  • Fenghong, Lu
    • Journal of the Korean Mathematical Society
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    • v.47 no.2
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    • pp.277-288
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    • 2010
  • The mixed chord-integrals are defined. The Fenchel-Aleksandrov inequality and a general isoperimetric inequality for the mixed chordintegrals are established. Furthermore, the dual general Bieberbach inequality is presented. As an application of the dual form, a Brunn-Minkowski type inequality for mixed intersection bodies is given.