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| 局部凸空间的平均局部一致凸性和一致光滑性 | |
| 引用本文： | 林尤武,魏文展,唐献秀,吴建功.局部凸空间的平均局部一致凸性和一致光滑性[J].广西科学,2011,18(3):201-206. |
| 作者姓名： | 林尤武 魏文展 唐献秀 吴建功 |
| 作者单位： | 1. 广西师范学院师园学院理科教学部,广西南宁,530001 2. 广西经贸职业技术学院,广西南宁,530021 3. 广东石油化工学院理学院,广东茂名,525000 |
| 摘 要： | 引进局部凸空间平均局部一致凸性的概念,给出其对偶的定义,即局部凸空间平均局部一致光滑性,并在p-自反的条件下得到它们之间的对偶定理,即(X,P)是平均局部一致凸(平均局部一致光滑)的当且仅当(X＇,P′)是平均局部一致光滑(平均局部一致凸)的. |
| 关 键 词： | 局部凸空间 平均局部一致凸性 平均局部一致光滑性 对偶关系 p-自反 |
| 收稿时间： | 2011/1/7 0:00:00 |
Average Locally Uniform Convexity and Uniform Smoothness in Locally Convex Spaces |
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| LIN You-wu,WEI Wen-zhan,TANG Xian-xiu and WU Jian-gong.Average Locally Uniform Convexity and Uniform Smoothness in Locally Convex Spaces[J].Guangxi Sciences,2011,18(3):201-206. | |
| Authors: | LIN You-wu WEI Wen-zhan TANG Xian-xiu and WU Jian-gong |
| Institution: | LIN You-wu1,WEI Wen-zhan2,TANG Xian-xiu3,WU Jian-gong1(1.Department of Science,Shiyuan College of Guangxi Teachers Education University,Nanning,Guangxi,530001,China,2.Guangxi Economic Trade Polytechnic,530021,3.College of Science,Guangdong University of Petrochemical Technology,Maoming,Guangdong,525000,China) |
| Abstract: | The definition of average locally uniform convexity in locally convex spaces is introduced,and we give the definition of average locally uniform smoothness in locally convex spaces as the dual of average locally uniform convexity.In addition,on the conditions of P-reflexivity,we obtained the dual relations between average locally uniform convexity and average locally uniform smoothness.Also,（X,P） is average locally uniform convexity（average locally uniform smoothness） if and only if（X′,P′） is average locally uniform smoothness（average local uniform convexity）. |
| Keywords: | locally convex spaces average locally uniform convexity average locally uniform smoothness dual theorem P-reflexivity |
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