A theorem on the minimization of a condensing multifunction and fixed points
type: Item
instance of: scholarly article
title: A theorem on the minimization of a condensing multifunction and fixed points
zbMATH Open document ID: 0602.47039
DOI: 10.1016/0022-247X(85)90355-5
author: V. M. Sehgal
author: S. P. Singh
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The main result of this paper is the following: Let E be a locally convex separated topological vector space. Let G be a subset of E with int(G)\(\neq \emptyset\), cl(G) convex and quasi-complete. If \(f:cl(G)\to P_{cp,cv}(E)\) is a continuous condensing multifunction with a bounded range, then for each \(w\in int(G)\) there exists a \(u=u(w)\) in cl(G) such that \(p(f(u)-u)=p(f(u)-cl(G))\), where p is the Minkowski' functional of (cl(G)-w). Further, if p(f(u)-w)\(\leq 1\) then \(u\in f(u)\) and if \(p(f(u)-w)>1\), then \(u\in \partial (cl(G))\).
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 3971579
zbMATH Keywords: fixed points
zbMATH Keywords: quasi-complete
zbMATH Keywords: continuous condensing multifunction with a bounded range
zbMATH Keywords: Minkowski' functional
reviewed by: Ioan A. Rus
MaRDI profile type: Publication
cites work: Extensions of two fixed point theorems of F. E. Browder
cites work: Fixed Point Theorems for Condensing Multifunctions
cites work: A Note on a Theorem of Ky Fan
cites work: Fixed points in locally convex spaces
cites work: On fixed point theorems obtained from existence theorems for differential equations
cites work: Approximate selections, best approximations, fixed points, and invariant sets
cites work: Fixed point theorems for set-valued mappings
cites work: Q3902047
cites work: Some Fixed Point Theorems for Condensing Multifunctions in Locally Convex Spaces
full work available at URL: 0022-247x(85)90355-5
OpenAlex ID: W2010888480
description: scientific article; zbMATH DE number 3971579