Journal of the
Korean Mathematical Society JKMS

For convex bodies, chord power integrals were introduced and studied in several papers (see [3], [6], 914], [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.

Keywords: convex body, chord power integrals, inclusion measure

MSC numbers: 52A40