In this paper,we first establish the dual Brunn-Minkowski inequality for the star duals for the Lp radial sum.Furthermore,we give some Brunn-Minkowski inequalities for the star duals of intersection bodies for the Lp radial sum and the Lp harmonic Blaschke sum.
Let K be a 1-unconditional convex bodies in Euclidean spaces.We study the asymptotic properties of two affine invariants m2（K） and S2（K） for a random simplex inside K.As an application,we discuss the asymptotic properties of two affine invariants m2（Bpn ） and S2（Bpn ）,where Bpn = {x ∈ Rn ： ‖x‖ p 1}.
