Abstract
In this article, some new inequalities about polar duals of convex and star bodies are established. The new inequalities in special case yield some of the recent results.MR (2000) Subject Classification: 52A30.
Highlights
In this article, some new inequalities about polar duals of convex and star bodies are established
We reserve the letter u for unit vectors, and the letter B for the unit ball centered at the origin
Let Sn denotes the set of star bodies in Rn
Summary
Some new inequalities about polar duals of convex and star bodies are established. We use V(K) for the n-dimensional volume of convex body K. h(K, ·) : Sn−1 → R, denotes the support function of K ∈ Kn; i.e., for u Î Sn-l h(K, u) = Max{u · x : x ∈ K}, (1:1) Let Sn denotes the set of star bodies in Rn. Let δdenotes the radial Hausdorff metric, as follows, if K, LÎ Sn, δ(K, L) = |ρK − ρL|∞ (See [1,2]). If K, L Î Sn, p ≥ 1, the Lp-dual mixed volume V −p(K, L) was defined by Lutwak (see [4]): V −p(K, L)
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