Convergence of decreasing sequences of convex sets in nonreflexive Banach spaces
type: Item
instance of: scholarly article
title: Convergence of decreasing sequences of convex sets in nonreflexive Banach spaces
zbMATH Open document ID: 0831.49016
DOI: 10.1007/BF01027825
author: Jonathan M. Borwein
author: A. S. Lewis
published in: Set-Valued Analysis
publication date: 1994-05-19T00:00:00Z
review text: A nested sequence of linear or convex closed sets of the form arising in estimation and other inverse problems is considered. It is shown that such a sequence may fail to converge in any of the recently studied set- convergences other than Mosco convergence. A positive result concerning the epislice convergence of related sequences of functions is provided.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 49K27
zbMATH DE Number: 558528
zbMATH Keywords: nonreflexive Banach spaces
zbMATH Keywords: convex closed sets
zbMATH Keywords: set-convergences
zbMATH Keywords: Mosco convergence
zbMATH Keywords: epislice convergence
Wikidata QID: Q56935910
reviewed by: Jaroslav Ramík
MaRDI profile type: Publication
cites work: The slice topology: a viable alternative to mosco convergence in nonreflexive spaces
cites work: Mosco and slice convergence of level sets and graphs of linear functionals
cites work: Partially finite convex programming. I: Quasi relative interiors and duality theory
cites work: Strong Rotundity and Optimization
full work available at URL: https://doi.org/10.1007/bf01027825
OpenAlex ID: W1986312424
description: scientific article; zbMATH DE number 558528