一种新度量下Veljan-Korchmaros型不等式的稳定性  

Stability of Veljan-Korchmaros Type Inequalities on a New Metric

作　　者：范芳芳[1] 王文[1] 朱儒进 张良辰[1] 丁致远 

机构地区：[1]合肥师范学院数学与统计学院,安徽合肥230061

出　　处：《合肥师范学院学报》2015年第3期10-15,共6页Journal of Hefei Normal University

基　　金：高等学校博士点专项科研基金项目(201134001110009);安徽省高校省级重点项目(KJ2013A220)

摘　　要：本文利用n维单形与其共超球的n维正则单形的偏差,引进了单行"R-偏差"度量的概念,从而证明了单行的Veljan-Korchmaros不等式,以及中面型和中线型Veljan-Korchmaros型不等式是稳定的,并给出这些几何不等式的稳定性版本。In this paper, the problem of the deviation regular metric is solved by introducing the definition of the R-deviation regular metric of an -simplex and an -dimensional regular simplex, which are in a sphere. The definition based on the fact that edge length of simplex plays an important role when defining the simplex. We prove that Veljian-Korchmaros type inequalities are all stable, and give the stability versions of these geometric inequalities for a simplex.

关 键 词：单行 外接球半径 内切球半径 Veljan-Korchmaros不等式 稳定性 

分 类 号：O178[理学—数学]