The mapping of compact into the set of its Chebyshev centres is Lipschitz in the space l^n_{\infty}

Local Lipschitz property of the map which puts in correspondence to N--net its Chebyshev center

We prove local Lipschitz property of the map which puts in correspondence to each $N$--net different from $(N-1)$--net its Chebyshev center. If dimension of Eucledean or Lobachevskii space is greater than 1 and net consists of more than 2 points we show that this map is not Lipschits in a neighbourhood of the space of 2--nets embedded into the space of all $N$--nets endowed by Hausdorff metric.

Almost bi--Lipschitz embeddings using covers of balls centred at the origin

In 2010, Olson \& Robinson [Transactions of the American Mathematical Society, 362(1), 145-168] introduced the notion of an almost homogeneous metric space and showed that if $X$ is a subset of a Hilbert space such that $X-X$ is almost homogeneous, then $X$ admits almost bi--Lipschitz embeddings into Euclidean spaces. In this paper, we extend this result and we show that if $X$ is a subset of a Banach space such that $X-X$ is almost homogeneous at the origin, then $X$ can be embedded in a Euclidean space in an almost bi--Lipschitz way.

广义 Fréchet 均值的一致一致性

Uniform Consistency of Generalized Fréchet Means

研究在具有 Heine-Borel 性质的度量空间上，通过凸损失函数定义的广义 Fréchet 均值的存在性、紧性、直径界和几乎必然一致性，并推导出损失函数类上的均匀强律。