LAUSR

In the paper, our main aim is to generalize Brunn-Mingkowski inequality for the mixed radial Blaschke–Minkowski homomorphisms into the Orlicz space. The fundamental notions and conclusions of the mixed radial Blaschke–Minkowski homomorphisms as well as related Brunn–Minkowski inequality are extended to an Orlicz setting. The new Orlicz–Brun–Minkowski inequality for the mixed radial Blaschke–Minkowski homomorphisms in special case yields the $$L_p$$ L p -Brunn–Minkowski inequality for mixed radial Blaschke–Minkowski homomorphisms, and mixed intersection bodies, respectively.