Equilibria of nonconvex valued maps under constraints
type: Item
instance of: scholarly article
title: Equilibria of nonconvex valued maps under constraints
zbMATH Open document ID: 1248.47051
author: Jarosław Mederski
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-03-16T00:00:00Z
review text: A notion of \(n\)-tangency is introduced for set-valued mappings in Banach spaces and some equilibrium theorems are given for this type of mappings. The main result is as follows. Theorem 2.3. If \(E\) is a Banach space, \(M\) is a compact and sleek \(\mathcal{L}\)-retract of \(E\) such that \(\chi(M)\neq 0\), \(\dim(M)\leq n+1\) and \(\varphi:M\to E\) is an \(n\)-tangent upper semi-continuous set-valued map, then there exists \(x_0\in M\) such that \(0\in \varphi(x_0)\).
reviewed by: Adrian Petruşel
Mathematics Subject Classification ID: 47H06
zbMATH DE Number: 6015239
zbMATH Keywords: equilibria
zbMATH Keywords: set-valued maps
zbMATH Keywords: approximations
zbMATH Keywords: sleek retracts
zbMATH Keywords: tangent maps
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.12.010
OpenAlex ID: W2003311310
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DOI: 10.1016/J.JMAA.2011.12.010
description: scientific article; zbMATH DE number 6015239