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

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