局部凸空间凸性和光滑性的几个等价定理

Equivalence Theorems of Convexity and Smoothness in Locally Convex Spaces

研究局部凸空间(X,P)的强凸性、非常凸性和严格凸性的等价关系,以及强光滑性、非常光滑性和光滑性的等价关系,由此得到若干凸性和光滑性的等价性定理,从而使Banach空间相平行的若干结果得到了推广。

Studies equivalence theorems of strong （very） convexity and strict convexity, strong （very） smoothness and smoothness are obtained in locally convex spaces （X, P） ,several convexity and smoothness equivalence theorems, generalizes corresponding notions and results in Banach space.