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In 2006, Schuster introduced the radial Blaschke-Minkowski homomorphisms. In this article, associating with the star duality of star bodies and dual quermassintegrals, we establish Brunn-Minkowski inequalities and monotonic inequality for the radial Blaschke-Minkowski homomorphisms. In addition, we consider its Shephard-type problems and give a positive form and a negative answer, respectively.

In this paper, we establish some inequalities for general chord-integrals of radial Blaschke-Minkowski homo- morphisms. As the applications, some inequalities for chord- integrals of intersection bodies are obtained. [ABSTRACT FROM AUTHOR]

The notion of radial Blaschke-Minkowski homomorphism was introduced by Schuster. In this paper, we study the radial Blaschke and radial Minkowski linear combinations, respectively, and give several inequalities under the notion of radial Blaschke Minkowski homomorphism in forms of star dual. [ABSTRACT FROM AUTHOR]

We establish some Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms with respect to Orlicz radial sums and differences of dual quermassintegrals. [ABSTRACT FROM AUTHOR]

In this paper we establish Minkowski, Brunn-Minkowski, and Aleksandrov-Fenchel type inequalities for volume differences of Blaschke-Minkowski homomorphisms and radial Blaschke-Minkowski homomorphisms. [ABSTRACT FROM AUTHOR]

In this article we first establish a dual isoperimetric type inequality for mixed radial Blaschke-Minkowski homomorphisms of different orders. Second, we prove a dual Brunn-Minkowski-type and a dual Minkowski-type inequality for mixed radial Blaschke-Minkowski homomorphisms. [ABSTRACT FROM AUTHOR]

Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms of star bodies and polar Blaschke-Minkowski homomorphisms of convex bodies are established. [ABSTRACT FROM AUTHOR]

In this paper we establish Minkowski, Brunn-Minkowski, and Aleksandrov-Fenchel type inequalities for volume differences of radial Blaschke-Minkowski homomorphisms. [ABSTRACT FROM AUTHOR]