General mixed chord-integrals of star bodies

Cyclic Brunn–Minkowski inequalities for general width and chord-integrals

“…Taking K 1 = · · · = K n-i = K and K n-i+1 = · · · = K n = B in (1.7) and allowing i to be any real, the general ith chord-integral C (τ ) i (K) of K ∈ S n o was given by (see [9])…”

Lp-dual affine surface areas for the general Lp-intersection bodies

“…Proof of Theorem 1.2. For K, L ∈ S n o , n ≥ 2, 0 < p < 1, 0 < q < n − p and τ ∈ [−1, 1], thus (n−p) 2 pq > 1, from (9) and (20), we get…”

Inequalities on General Lp-Mixed Chord Integral Difference

“…In 1977, Lutwak introduced the notion of a mixed width-integral of convex bodies (see [7]), and the dual notion, mixed chord-integrals of star bodies was defined by Lu (see [8]). Later, as a part of the asymmetric L p Brunn-Minkowski theory, which has its origins in the work of Ludwig, Haberl and Schuster (see [9][10][11][12][13]), Feng and Wang generalized the mixed chord-integrals to general mixed chord-integrals of star bodies (see [14]). For K 1 , • • • , K n ∈ S n 0 and τ ∈ (−1, 1), the general mixed chord-integral…”