涉及单形内点几个不等式的稳定性  

Stability of Several Inequalities Involving Interior Points of a Simplex

作　　者：孙玉婷[1] 王文[2] 杨世国[3] SUN Yu-ting;WANG Wen;YANG Shi-guo(College of Liberal Studies,Anhui Wenda University of Information Engineering,Hefei,Anhui,231201;Hefei Normal University,Hefei,Anhui,230601;Anhui Xinhua University,Hefei,An-hui,230088)

机构地区：[1]安徽文达信息工程学院通识教育学院,安徽合肥231201 [2]合肥师范学院,安徽合肥230601 [3]安徽新华学院,安徽合肥230088

出　　处：《韩山师范学院学报》2022年第6期9-16,共8页Journal of Hanshan Normal University

基　　金：安徽省自然科学基金项目(项目编号:1908085QA04);安徽文达信息工程学院校级一般科研项目(项目编号:XZR2019B02)。

摘　　要：利用单形的“偏正度量”和几何不等式理论,研究欧氏空间En中n维单形几何不等式的稳定性,证明了三个涉及单形内点的不等式是稳定的,同时给出相应的稳定性版本.从而为一般凸体的稳定性研究奠定基础.By using the deviation regular metric and the theory of geometric inequality,the stability of some geometric inequalities for an n-simplex in the Euclidean space En is studied. It is proved that three geometric inequalities are stable,and the stability versions of inequality are given. Therefore,the study lays a foundation for the study on the stability of general convex bodies.

关 键 词：偏正度量 稳定性 单形 内点 

分 类 号：G623[文化科学—教育学]