The stability of some geometric inequalities for a simplex

Using the theory and methods of metric geometry to study the problems of stability,which is some geometric inequalities for an n-simplex in the n-dimensional Euclidean space En.From the deviation regular metric of two simplexes,we prove that Sallee-Alexander's and Yang-Zhang's inequalities for the width of an n-simplex are all stable,and also prove that Veljan-Korchmaros's inequalities for the medians and the middle sections of an n-simplex are all stable.The stability versions of these geometric inequalities for a simplex are established,and these geometric inequalities are improved.