广义L_(p)宽度积分的混合Brunn-Minkowski型不等式  

Mixed Brunn-Minkowski Type Inequalities of General L_(p) Width-Integral

作　　者：杨林 谭杨[1] 罗淼 YANG Lin;TAN Yang;LUO Miao(Department of Information Technology, Tongren Polytechnic College, Tongren, Guizhou 554300, China;School of Mathematics Science, Guizhou Normal University, Guiyang 550025, China)

机构地区：[1]铜仁职业技术学院信息工程学院,贵州铜仁554300 [2]贵州师范大学数学科学学院,贵阳550025

出　　处：《西南师范大学学报（自然科学版）》2022年第2期37-42,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：2019年度贵州省基础研究计划(黔科合基础[2019]1228号);铜仁市科研项目([2020]116号).

摘　　要：研究了凸几何分析中的广义L_(p)宽度积分,利用Hölder不等式与Minkowski不等式把欧氏空间中宽度积分的Brunn-Minkowski型不等式推广为关于L_(p)宽度积分的混合型Brunn-Minkowski型不等式.同时给出了逆向的关于L_(p)宽度积分的混合型Brunn-Minkowski型不等式,并研究了等号成立的条件.In this paper,the general L_(p) width integral in convex geometric analysis has been studied.By using the Hölder inequality and Minkowski inequality,the Brunn-Minkowski type inequality in Euclidean space has been generalized to the mixed Brunn-Minkowski type inequality of the L_(p) width integral.An inverse mixed Brunn-Minkowski type inequality of the L_(p) width integral and its equal condition have been given.

关 键 词：广义L_(p)宽度积分 Hölder不等式 MINKOWSKI不等式 BRUNN-MINKOWSKI不等式 

分 类 号：O186.5[理学—数学]