Multivalued maps and the existence of best approximants
type: Item
instance of: scholarly article
title: Multivalued maps and the existence of best approximants
zbMATH Open document ID: 0729.41027
DOI: 10.1016/0021-9045(91)90074-K
author: N. E. Zubov
published in: Journal of Approximation Theory
publication date: 1991-01-01T00:00:00Z
review text: The authors give the following generalization of \textit{Ky Fan}'s well- known result [Extensions of two fixed point theorems of F. E. Browder, Math. Z. 112, 234-240 (1969; Zbl 0185.395)]: Let X be a Banach space and let M be an approximatively compact and convex subset of X. Let f: \(M\to X\) be a continuous map such that f(M) is relatively compact. Let g: \(M\to M\) be a continuous onto and proper map such that \(g^{-1}(z)\) is an acyclic subset of M for every \(z\in M\). Then there exists \(x\in M\) so that \(\| g(x)-f(x)\| d(f(x),M).\) Some interesting consequences are also pointed out.
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 4205069
zbMATH Keywords: Ky Fan's theorem
zbMATH Keywords: multivalued maps
reviewed by: Silvestru Sever Dragomir
MaRDI profile type: Publication
cites work: Topological degree and nonlinear mappings of analytic type in Banach spaces
cites work: Q5185568
cites work: Extensions of two fixed point theorems of F. E. Browder
cites work: Lefschetz fixed point theorems for a new class of multi-valued maps
cites work: Fixed-point theorems for set-valued mappings and existence of best approximants
cites work: Approximate selections, best approximations, fixed points, and invariant sets
cites work: A theorem on best approximations
cites work: Q5595759
description: scientific article; zbMATH DE number 4205069