On nonexistence of strongly unique best approximations
type: Item
instance of: scholarly article
title: On nonexistence of strongly unique best approximations
zbMATH Open document ID: 0689.41028
DOI: 10.1016/0022-247X(89)90161-3
author: Ryszard Smarzewski
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: The author proves the following theorems: If M is an n-dimensional subspace of a real normed linear space X and if \(x\in X\setminus M\) and \(m\in M\) are such that \(\dim F(x-m)\leq n\) (where \(F(z)=\{f\in X^*:\quad \| f\| =1,\quad f(z)=\| z\| \}),\) then m is not a strongly unique best approximation in M to x. If there is a \(z\neq 0\) in a real normed linear space x such that dim F(z)\(=n\), then there exists an n- dimensional space M of X, an element \(x\in X\setminus M\), and a strongly unique best approximation m in M to x.
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 4129394
zbMATH Keywords: strongly unique best approximation
MaRDI profile type: Publication
cites work: Q4159877
cites work: Q3254057
cites work: Q5583334
cites work: Uniqueness and strong uniqueness of best approximations by spline subspaces and other subspaces
cites work: Uniqueness and Differential Characterization of Approximations from Manifolds of Functions
description: scientific article; zbMATH DE number 4129394