关于K-强凸空间  

ON K -STRONGLY CONVEX SPACES

作　　者：苏雅拉图[1] 

机构地区：[1]内蒙古师范大学数学系

出　　处：《内蒙古师范大学学报（自然科学汉文版）》1999年第2期101-105,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：内蒙古教育厅科研基金

摘　　要：进一步研究了Ｋ－强凸空间的几何性质，证明了光滑的Ｋ－强光滑空间是强光滑的；严格凸的Ｋ－强凸空间是强凸的；若Ｘ是Ｋ－强凸空间，则Ｘ具有（Ｋ）性质，进而严格凸的Ｋ－强凸空间具有（Ｇ）性质；若Ｘ是ＬωＲ（ＬＫＲ）空间，则Ｘ是强凸空间．In 1998,we introduced the K strongly convex space and obtained many results about them.In this paper,we further studied the geometric properties of K strongly convex space,and proved that every smooth K strongly smooth space is strongly smooth space.Every strictly convex K strongly convex space is strongly convex space.If X is K strongly convex space then X has the property(K),furthermore,strictly convex K strongly convex space has the property(G). If X is LωR(LKR) space then X is strongly convex space.These results generalized the results of Suyalatu,Lovaglia,Yu Xintai and Wang Jianhua.

关 键 词：K-强凸空间 强凸空间 强光滑性 巴拿赫空间 

分 类 号：O177.3[理学—数学] O177.2[理学—基础数学]