Well-posedness and porosity in best approximation problems
Keywords
Banach space, complete metric space, generic property, hyperbolic space, nearest point, porous setAbstract
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.Downloads
Published
2001-12-01
How to Cite
1.
REICH, Simeon and ZASLAVSKI, Alexander J. Well-posedness and porosity in best approximation problems. Topological Methods in Nonlinear Analysis. Online. 1 December 2001. Vol. 18, no. 2, pp. 395 - 408. [Accessed 13 November 2024].
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