局部凸空间的平均局部一致凸性和一致光滑性

Average Locally Uniform Convexity and Uniform Smoothness in Locally Convex Spaces

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.

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）.