Topological Methods in Nonlinear Analysis

Well-posedness and porosity in best approximation problems

Simeon Reich and Alexander J. Zaslavski

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Abstract

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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 18, Number 2 (2001), 395-408.

Dates
First available in Project Euclid: 22 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1471876708

Mathematical Reviews number (MathSciNet)
MR1911709

Zentralblatt MATH identifier
1005.41011

Citation

Reich, Simeon; Zaslavski, Alexander J. Well-posedness and porosity in best approximation problems. Topol. Methods Nonlinear Anal. 18 (2001), no. 2, 395--408. https://projecteuclid.org/euclid.tmna/1471876708


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