Hahn-Banach定理在凸性模定义中的应用

An Application of Hahn-Banach's Theorem to Modulus of Convexity

该文利用Ｈａｈｎ－Ｂａｎａｃｈ定理得到了凸性模定义中若干等式的证明，并且指出对维数不小于２的实线性赋范空间Ｘ，有下面类似的等式成立其中且０＜＜２，０＜ａ＜１．

In this paper, some equalities in the defination of modulus of convexity are easily proved by Hahn-Banach's theorem, on the other hand, the following similar equalities are also obtained for real normed linear space with dim where