General L p $L_{p}$ -mixed chord integrals of star bodies

Abstract

Abstract The notion of general mixed chord integrals of star bodies was introduced by Feng and Wang. In this paper, we extend the concept of the general mixed chord integrals to general L p $L_{p}$ -mixed chord integrals of star bodies. Based on this new notion, we study their extremum values and obtain an Aleksandrov-Frenchel type and a cyclic inequality for general L p $L_{p}$ -mixed chord integrals of star bodies, respectively. Further, as applications, we establish two Brunn-Minkowski type inequalities for L p $L_{p}$ -radial bodies. Finally, we get an interesting identical equality on combining L p $L_{p}$ -radial bodies.

Keywords

• star body
• mixed chord integrals
• general L p $L_{p}$ -mixed chord integrals
• L p $L_{p}$ -radial body