局部凸空间P-自反下的中点局部k-一致凸性(光滑性)

Midpoint Locally k-Uniformly Convexity (Smoothness) Condition Under P-Reflexivity on Locally Convex Spaces

在局部凸空间已有的中点局部kk-一致凸性和中点局部k-一致光滑性这一对对偶概念的基础上,证明了中点局部kk-一致凸性与中点局部(k+1)-一致凸性的关系,给出了在P-自反的条件下它们之间的等价对偶定理.

At the base of midpoint locally k-uniformly convexity and midpoint locally k-uniformly smoothness, proved the relationship between midpoint locally k-uniformly convexity and midpoint locally（k＋1）-uniformly convexity, then on the conditions of P-reflexivity,we obtain further the equivalont dual theorem of between midpoint locally k-uniformly convexity and midpoint locally k-uniformly smoothness.