局部凸空间的平均强凸性的等价刻画

Equivalent Characterizations of Average Strong Convexity in Locally Convex Spaces

引进了局部凸空间平均强凸的概念,它既是Banach空间平均强凸性在局部凸空间的推广,又是局部凸空间强凸性概念的自然推广;得到了平均强凸的局部凸空间的特征刻画;同时也探讨了它与其它一些凸性的关系.

We introduced the average strong convexity in locally convex spaces, which is the generalization of both strong convexity in Banach spaces and strong convexity in locally convex spaces. In addition, we obtained some necessary and sufficient conditions of strong convexity in locally convex spaces. At the same time, we discussed the relationship between this convexity and some other convexities.