关于Sallee-Alexander不等式与Veljan-Korchmaros不等式新的稳定性版本  

New Stability Versions of Sallee-Alexander Inequality and Veljan-Kochmaros Inequality

作　　者：陈士龙[1] 

机构地区：[1]安徽广播影视职业技术学院基础教学部,安徽合肥230011

出　　处：《安徽理工大学学报（自然科学版）》2017年第1期81-86,共6页Journal of Anhui University of Science and Technology:Natural Science

基　　金：安徽省自然科学重点科研项目(KJ2015A351)

摘　　要：利用单形的"偏正"度量与几何不等式理论,研究欧氏空间En中关于n维单形的SalleeAlexander不等式与Veljan-Korchmaros不等式的稳定性,利用cscθ≥1的性质,获得它们新的稳定性版本,将原有的稳定性版本推广为对(n维单形Ω,τ∈[2,n],有(W(Ω))-2 n2-1)≥(cscθ)1/(n-1)2[βn(n+1)n+1/n/n(n!)2/nV-2/n]n2-1+λ(n,τ)·δ(Ω,Ω)和(W(Ω))-2(n2-1)≥(cscθ)1/(n-1)2(βnR-2)n2-1+λ(n,τ)·δ(Ω,Ω),证明它们是稳定的,推广了这些不等式得出了相应的推论。By using the deviation regular metric and theory of geometric inequalities as a simplex sions of Sallee - Alexander inequality and Veljan - Kochmaros inequality for an n - simplex the stability ver- in the Euclidean space En were studied. With the characteristic being csc0 〉 1, the new stability versions of these inequalities were obtained. For n n -simplex in the Euclidean space E＂, the inequalities （W（Ω））-2 n2-1）≥（cscθ）1/（n-1）2[βn（n＋1）n＋1/n/n（n!）2/nV-2/n]n2-1＋λ（n,τ）·δ（Ω,Ω）和（W（Ω））-2（n2-1）≥（cscθ）1/（n-1）2（βnR-2）n2-1＋λ（n,τ）·δ（Ω,Ω）, , were acquired, which are proved stable and the relative theories are gotten with their generalization

关 键 词：欧氏空间 单形 宽度 体积 稳定性版本 

分 类 号：O184[理学—数学]