Description

• Title:
  Well-posedness and porosity in best approximation problems
• Creator:
  Reich, Simeon;
  Zaslavski, Alexander J.
• Description:
  Given a nonempty closed subset $A$ of a Banach space $X$ and a point $x \in X$, we consider the problem of finding a nearest point to $x$ in $A$. We define an appropriate complete metric space $\mathcal M$ of all pairs $(A,x)$ and construct a subset $\Omega$ of $\mathcal M$ which is the countable intersection of open everywhere dense sets such that for each pair in $\Omega$ this problem is well-posed. As a matter of fact, we show that the complement of $\Omega$ is not only of the first category, but also sigma-porous.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2001.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 18, No 2 (December 2001); 395 - 408;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2001.041/9932
• Subject:
  Banach space;
  complete metric space;
  generic property;
  hyperbolic space;
  nearest point;
  porous set;
  41A50;
  41A52;
  41A65;
  54E35;
  54E52
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2001.041
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other