Stable approximations of set-valued maps
type: Item
instance of: scholarly article
title: Stable approximations of set-valued maps
zbMATH Open document ID: 0681.54012
DOI: 10.1016/S0294-1449(16)30334-1
author: Jean-Pierre Aubin
author: Roger J.-B. Wets
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78163
review text: The aim of this paper is an extension of the Lax' principle: ``stability and consistency implies convergence'' to the case of general inclusion \(y_ 0\in F(x_ 0)\) where F is a multifunction from a Banach space X to a Banach space Y, \(y_ 0\in Y\). If \(X_ n\), \(Y_ n\) are some approximations of the space X and Y respectively, \(y_ n\in Y_ n\) approximates \(y_ 0\) and if \(F_ n\) are ``consistent with F'', an adequate stability property of the sequence \(\{F_ n\}\) implies the convergence of some sequence \(\{x_ n\}\) of solutions of the inclusions \(y_ n\in F(x_ n)\), \(n=1,2,..\). to \(x_ 0\). This stability is based on the properties of contingent derivative of multifunctions. An extension of the Banach-Steinhaus theorem to the set-valued analogues of linear, continuous operators is also proved.
reviewed by: Z.Wyderka
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 93D99
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 4115509
zbMATH Keywords: graph convergence
zbMATH Keywords: nonlinear inlusions
zbMATH Keywords: stability
zbMATH Keywords: contingent derivative
Wikidata QID: Q103677942
MaRDI profile type: Publication
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OpenAlex ID: W2591477748
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description: scientific article; zbMATH DE number 4115509