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Sallee-Alexander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,T∈[2,n],有(W(Ω))-2(n2-1)≥(cscθ)1(n-1)2[βn(n+1)n+1nn(n!)2nV-2n]n2-1+λ(n,T)·δ(Ω,)和(W(Ω))-2(n2-1)≥(cscθ)1(n-1)2(βnR-2)n2-1+λ(n,T)·δ(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 the stability versions of Sallee-Alexander inequality and Veljan-Kochmaros inequality for an n-simplex in the Euclidean space En were studied.With the characteristic being cscθ≥1, the new stability versions of these inequalities were obtained.For n n-simplex in the Euclidean space En ,the inequalities (W(Ω))-2(n2-1)≥(cscθ)1(n-1)2[βn(n+1)n+1nn(n!)2nV-2n]n2-1+λ(n,T)·δ(Ω,)and (W(Ω))-2(n2-1)≥(cscθ)1(n-1)2[βnR-2)n2-1+λ(n,T)·δ(Ω,T∈[2,n],were acquired,which are proved stable and the reative theories are gotten with their generalization.