范数平面上三点集的费马-托里拆利问题

Q4 Mathematics

Chebyshevskii Sbornik Pub Date : 2022-10-09 DOI:10.22405/2226-8383-2022-23-5-72-86

D. A. Ilyukhin

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引用次数: 1

摘要

本文考虑了费马-托里拆利问题。这个问题要求一个点最小化到d维实赋范空间中任意给定点的距离之和。本文概述了这一问题的各种概括，介绍了目前解决这一问题的方法和最近的一些结果。本文的目的是寻找以下问题的答案:在平面上的什么范数下，费马-托里拆利问题的解对任意三点唯一。文中给出了唯一性判据，并给出了唯一性判据在正多边形(即平面)所定范数上的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Fermat-Torricelli problem in the case of three-point sets in normed planes

In the paper the Fermat-Torricelli problem is considered. The problem asks a point minimizing the sum of distances to arbitrarily given points in d-dimensional real normed spaces. Various generalizations of this problem are outlined, current methods of solving and some recent results in this area are presented. The aim of the article is to find an answer to the following question: in what norms on the plane is the solution of the Fermat-Torricelli problem unique for any three points. The uniqueness criterion is formulated and proved in the work, in addition, the application of the criterion on the norms set by regular polygons, the so-called lambda planes, is shown.

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来源期刊

Chebyshevskii Sbornik Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The aim of the journal is to publish and disseminate research results of leading scientists in many areas of modern mathematics, some areas of physics and computer science.