Isotone retraction cones in Hilbert spaces
type: Item
instance of: scholarly article
title: Isotone retraction cones in Hilbert spaces
zbMATH Open document ID: 1241.46001
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-06-11T00:00:00Z
review text: Let \(H\) be a Hilbert space and equip \(H\) with the ordering induced by a pointed closed convex cone. So, a mapping on \(H\) is said to be \textit{isotone} if it is monotonically increasing. The notion of sharp mappings is introduced in this note. It is shown then that a pointed closed generating convex cone in \(H\) is latticial if and only if there is a continuous retraction onto the cone with a sharp complement. Particular cases and examples are given throughout. The problem discussed in this note is connected with a series of papers given by the author and Isaac over the last three decades. For more details, the reader is referred to this interesting note and its list of references.
reviewed by: Karim Boulabiar
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 5720178
zbMATH Keywords: isotone mapping
zbMATH Keywords: retractions
zbMATH Keywords: isotone retraction cones
zbMATH Keywords: sharp mapping
zbMATH Keywords: latticial cones
zbMATH Keywords: projection onto cones
zbMATH Keywords: isotone projection cones
author: S. Z. Németh
MaRDI profile type: Publication
full work available at URL: j.na.2010.03.044
OpenAlex ID: W2091069904
cites work: Monotonicity of metric projection onto positive cones of ordered Euclidean spaces
cites work: Every generating isotone projection cone is latticial and correct
cites work: Q5751411
cites work: Projection methods, isotone projection cones, and the complementarity problem
cites work: Q4020377
cites work: Inequalities characterizing coisotone cones in Euclidean spaces
cites work: In what spaces is every closed normal cone regular?
cites work: Q3845569
cites work: Characterization of a Hilbert vector lattice by the metric projection onto its positive cone
cites work: Regular exceptional family of elements with respect to isotone projection cones in Hilbert spaces and complementarity problems
cites work: Iterative methods for nonlinear complementarity problems on isotone projection cones
DOI: 10.1016/J.NA.2010.03.044
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description: scientific article; zbMATH DE number 5720178