Dual Orlicz Hausdorff Metrics And Dual Mixed Brightness-integrals Of Star Bodies

In this thesis we investigate the dual Orlicz Hausdorff metric and the dual mixed brightness-integral of star bodies.Firstly,we introduce a new metric for star bodies and provide a connection of it with the classical dual Hausdorff metric and the 1 dual Hausdorff metric.This newly-introduced metric provides the possibility of calculating the distance between two star bodies in the Orlicz setting.Secondly,we study the dual mixed brightness integrals of star bodies and their associated extreme problems.We establish the cyclic inequality and the connection between this quantity and the volume of the intersection body of the involved star bodies.