Dual Orlicz–Brunn–Minkowski theory: Dual Orlicz Lϕ affine and geominimal surface areas

This paper aims to develop the basic theory for the dual Orlicz LϕLϕ affine and geominimal surface areas of star bodies. Basic properties of these new affine invariants are established. Moreover, related Orlicz affine isoperimetric, cyclic, Santaló type and Alexandrov–Fenchel type inequalities are obtained.