一致凸性与选择的分裂问题
Uniform convexity and the splitting problem for selections
摘要：
我们继续调查的情况下，Repovenski-Semenov分裂问题的选择有一个肯定的解决方案，连续集值映射。我们考虑无限维一致凸巴拿赫空间中的情形。我们使用Polyak的一致凸性和模的一致凸性的任意凸集（不必要的球）的概念。研究了一致凸集的一般几何性质。我们还得到了具有一致凸象的集值映射的选择分裂问题的一个肯定解。
英文摘要：
We continue to investigate cases when the Repovš-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images.
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