论文标题
规范线性空间中最远的点问题和部分统计连续性
Farthest Point Problem and Partial Statistical Continuity in Normed Linear Spaces
论文作者
论文摘要
在本文中，我们证明，如果$ e $是一个真正的遥远的遥控子集的一个真实的线性空间$ x $的子集，使得$ e $具有x $中的chebyshev中心$ c \ in x $，而最远的点映射$ f：x \ rightarrow e $限于$ [c，f（c）$是$ c $ c $ $ e $ e a a n in a n in a $ e a a n in a n in IS a a nece $ e a a a a necy as a a a nece $ e a a a a n nistect a a a n n in n IS a a nececon a a n nistlecon。我们在统一的圆形Banach空间的独特远程子集上获得了必要的条件。此外，我们表明存在一个具有Chebyshev Center $ C $的远程集合$ M $，因此最远的点映射$ f：\ Mathbb {r} \ rightArrow m $在$ c $时不连续，但在多估计意义上是部分统计上统计上统计上连续的。
In this paper, we prove that if $E$ is a uniquely remotal subset of a real normed linear space $X$ such that $E$ has a Chebyshev center $c \in X$ and the farthest point map $F:X\rightarrow E$ restricted to $[c,F(c)]$ is partially statistically continuous at $c$, then $E$ is a singleton. We obtain a necessary condition on uniquely remotal subsets of uniformly rotund Banach spaces to be a singleton. Moreover, we show that there exists a remotal set $M$ having a Chebyshev center $c$ such that the farthest point map $F:\mathbb{R}\rightarrow M$ is not continuous at $c$ but is partially statistically continuous there in the multivalued sense.
