Fixed point theorems and invariant approximations
type: Item
instance of: scholarly article
title: Fixed point theorems and invariant approximations
zbMATH Open document ID: 0673.41037
DOI: 10.1016/0021-9045(89)90113-5
author: Leopold Habiniak
published in: Journal of Approximation Theory
publication date: 1989-01-01T00:00:00Z
review text: Let S be a closed, star-shaped subset of normed linear space E, and let T: \(S\to S\) be a nonexpansive mapping. The author first observes that if cl(T(S)) is compact, then T has a fixed point. As a consequence, he proves that if A: \(E\to E\) is a nonexpansive mapping with fixed point a which leaves invariant a subspace M of E, and if A takes bounded subsets of M to relatively compact subsets, then the point a has a best approximation in M which is also a fixed point of A.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 58C30
zbMATH DE Number: 4101815
zbMATH Keywords: nonexpansive mapping
reviewed by: Richard M. Aron
MaRDI profile type: Publication
full work available at URL: 0021-9045(89)90113-5
OpenAlex ID: W1998390010
cites work: Fixed Point Theorems for Non-Expansive Mappings on Star-Shaped Subsets of Banach Spaces
cites work: Invarianz bei linearen Approximationen
cites work: Q3326212
cites work: An application of a fixed point theorem to best approximation
description: scientific article; zbMATH DE number 4101815