局部凸空间的中点局部k-一致凸性与中点局部k-一致光滑性

引入局部凸空间的中点局部k-一致凸性和中点局部k-一致光滑性这一对对偶概念,它们既是Banach空间中点局部k-一致凸性和中点局部k-一致光滑性推广,又是局部凸空间中点局部一致凸性和中点局部一致光滑性的自然推广。讨论它们与其它k-凸性(k-光滑性)之间的关系。

Midpoint Locally k-Uniformly Convexity and Midpoint Locally k-Uniformly Smoothness in Locally Convex Spaces

The dual notions of midpoint locally k-uniformly convexity and midpoint locally k-uniformly smooth on Locally Convex Spaces are introduced , which are generalizations of both midpoint locally k-uniformly convexity (midpoint locally k-uniformly smoothness) in Banach spaces and midpoint locally uniformly convexity (midpoint locally uniformly smoothness) in locally convex spaces. The relationship between them and the other convexity (smoothness) are discussed.