Scholarlink

Abstract <p> It is shown that, in many problems of geometric approximation theory related to min- and max-approximative compactness, it suffices to consider not the entire unit sphere, but rather its only part consisting of acting points (for a given set <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3227_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(M\)</EquationSource> </InlineEquation>) — these being the points of the unit sphere such that <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11503_2025_3227_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(M\)</EquationSource> </InlineEquation> can be touched by an “analog” of such a point on some homothetic copy of the unit ball. CLUR- and VDS-point for a set are introduced, and their relations to points of min- and max- approximative (norm, weak) compactness are studied. In terms of these points, balayage theorems for problems of min- and max- approximative (norm, weak) compactness of suns and max-suns are obtained. </p> <p> <b> DOI</b> 10.1134/S1061920825600527 </p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Approximative Compactness and Acting Points

  • 期刊论文

  • 发表日期：

    2025年6月1日

查看全文
  • A.R. Alimov,
  • N.A. Ilyasov

摘要

Abstract

It is shown that, in many problems of geometric approximation theory related to min- and max-approximative compactness, it suffices to consider not the entire unit sphere, but rather its only part consisting of acting points (for a given set \(M\) ) — these being the points of the unit sphere such that \(M\) can be touched by an “analog” of such a point on some homothetic copy of the unit ball. CLUR- and VDS-point for a set are introduced, and their relations to points of min- and max- approximative (norm, weak) compactness are studied. In terms of these points, balayage theorems for problems of min- and max- approximative (norm, weak) compactness of suns and max-suns are obtained.

DOI 10.1134/S1061920825600527