$L_{p}$-dual Brunn–Minkowski inequality for intersection bodies

In 2003, associated with the radial Minkowski additions of star bodies, Zhao and Leng established the dual Brunn–Minkowski inequality for intersection bodies. In this paper, associated with the L_{p} -radial Minkowski combinations of star bodies, we firstly prove the L_{p} -dual Brunn–Minkowski inequality for intersection bodies. Further, associated with the L_{p} -Minkowski combinations of convex bodies, we give the L_{p} -Brunn–Minkowski inequality for star dualities of intersection bodies.