Orlicz Mixed Brightness-Integral And Related Inequalities

The main content of convex geometry analysis research is Brunn-Minkowski theory,which is widely concerned in the world.After the classical Brunn-Minkowski theory,it has developed into Lp-Brunn-Minkowski theory and dual Lp-Brunn-Minkowski theory.In recent ten years,the development of Orlicz-Brunn-Minkowski theory and dual Orlicz-BrunnMinkowski theory has aroused great interest of many mathematicians at home and abroad.The research of this dissertation is based on Lp-Brunn-Minkowski theory and Orlicz-BrunnMinkowski theory.In the first chapter,we mainly introduce the development history of Brunn-Minkowski theory and related research results,as well as some symbolic meanings and article structure of this paper.In the second chapter of this dissertation,we obtain the Brunn-Minkowski type inequality of i-th general Lp-mixed width integral and i-th general Lp-mixed chord integral,the difference cyclic type inequality of i-th general Lp-mixed width integral and i-th general Lp-mixed chord integral,the cyclic type Brunn-Minkowski of i-th general Lp mixed-width integral and i-th general Lp-mixed chord integral,and the difference cyclic type inequality of general Lp-mixed width integral and general Lp-mixed chord integral.In the third chapter,under the influence and inspiration of the development of OrliczBrunn-Minkowski theory,we first give the definition of Orlicz-brightness addition and Orliczbrightness linear combination,and derive a series of useful properties.On this basis,we get an integral definition expression of Orlicz-mixed brightness integral.Thus,the brightness integral is extended to Orlicz space,and Orlicz-brightness Minkowski type inequality,Orlicz-brightness Brunn-Minkowski type inequality and related corollaries are also established.In the fourth chapter,we make a summary of the main work of this paper and look forward to the possible future work.