局部凸空间的平均一致凸性与平均一致光滑性  

Average Uniform Convexity and Average Uniform Smoothness in Locally Convex Spaces

作　　者：林尤武[1] 魏文展[2] 唐献秀[1] 

机构地区：[1]广西师范学院数学与计算机科学系,广西南宁530023 [2]广西经贸职业技术学院,广西南宁530021

出　　处：《广西科学》2009年第1期17-22,共6页Guangxi Sciences

基　　金：广西自然科学基金项目[桂科自0728050]资助

摘　　要：引进局部凸空间的平均一致凸性的概念,给出其对偶的定义,得到平均一致凸(平均一致光滑)的局部凸空间的特征刻画及其在P-自反条件下的对偶关系:(X,P)是平均一致凸(平均一致光滑)的当且仅当(X′,P′)是平均一致光滑(平均一致凸)的.The definition of average uinform converxity in locally conver spaces is introduced,and we give the definition of average uniform smoothness in locally conver spaces as the dual of average uniform converxity, and obtained some necessary and sufficient conditions of average uinform converxity （average uniform smoothness） in locally conver spaces. In addition,on the conditions of P-reflexivity,we obtained the dual relations of between average uinform converxity and average uniform smoothness,also, （X,P） is average uinform converxity （average uinform smoothness） if and only if （X′, P′）） is average uinform smoothness （average uinform converxity）.

关 键 词：局部凸空间 平均一致凸性 平均一致光滑性 对偶关系 P-自反 

分 类 号：O177[理学—数学]