The $$({\varvec{q}},\varvec{\phi })$$ ( q , ϕ ) -Dual Orlicz Mixed Affine Surface Areas

Abstract

Based on the $$(q,\phi )$$ -dual Orlicz mixed volume which was introduced by Gardner et al., we pose a new concept called $$(q,\phi )$$ -dual Orlicz mixed affine surface areas, whose special case is just $$L_p$$ dual affine surface areas. Further, some related inequalities involving product inequality, cyclic inequality and Brunn–Minkowski inequality are established, respectively.