  In 1970, Schneider introduced the higher-order difference body and the
associated Rogers-Shephard inequality. Recently, Haddad, Langharst, Putterman,
Roysdon and Ye expanded the concept to a burgeoning higher-order
Brunn-Minkowski theory. In 1991, Zhang introduced mean zonoids of a convex
body, which was extended to the Firey-Brunn-Minkowski theory setting by Xi, Guo
and Leng in 2014. In this note, we extend these $L^p$ mean zonoids to the
higher-order setting and establish the associated isoperimetric inequality.
