局部凸空间k-强光滑性与k-非常光滑性的进一步探讨

Further Exploration on k-Strongly Smoothness and k-Extremely Smoothness In Locally Convex Spaces

给出局部凸空间强光滑性和非常光滑性的等价定义,由此修正了k-强光滑性与k-非常光滑性的概念,并证明k-强光滑(k-非常光滑)蕴含k+1-强光滑(k+1-非常光滑),严格推广了Banach空间相应概念和结果.

We give the equivalent notions of the strongly smoothness and extremely smoothness for locally convex spaces,and notions of the k-strongly smoothness and k-extremely smoothness are obtained,k-strongly smoothness（k-extremely smoothness）implies k＋1-strongly smoothness（k＋1-extremely smoothness） are proved,corresponding notions and results in Banach space is generalized.