摘要
本文引入了一种新的K凸空间K-非常凸空间,及其对偶空间K-非常光滑空间,它们分别是非常凸空间和非常光滑空间的推广但又严格弱于非常凸空间和非常光滑空间,因此它们又有许多独特的性质.本文讨论了它们的一些特性及与其它K凸性和K光滑性的关系,推广了[3]、[6]、[7]、[8]中的一些结果.
In this paper we introduce a new K convex space, that is K-very convex space with K smooth dual space. The new K convex space and K smooth space are strictly weaker than the old ones. We discuss their properties and the relationship with other K convexities or K smoothness. We generalize some known results.
基金
香港中山大学高等学术研究中心基金会资助项目(04M1O)
关键词
K-非常凸
K-非常光滑
中点局部K-致凸
弱中点局部K-致凸
K-严格凸
K-very convex
K-very smooth
K-strictly convex
midpoint locally K uniformly convex
weakly midpoint locally K uniformly convex.
