The essential components of coincident points for weakly inward and outward set-valued mappings
type: Item
instance of: scholarly article
title: The essential components of coincident points for weakly inward and outward set-valued mappings
zbMATH Open document ID: 0955.47040
DOI: 10.1016/S0893-9659(99)00046-4
author: G. Isac
author: George Xian-Zhi Yuan
published in: Applied Mathematics Letters
publication date: 2001-02-14T00:00:00Z
review text: The paper concerns a semicontinuous dependence on \(y=(f,g)\) of the coincident set \(F(y)=\{x\in X;f(x)\cap g(x)\neq\emptyset\}\) where \(f:X\to X\) and \(g:X\to X\) are set-valued mappings. Precisely, \(X\) is a nonempty compact convex set of a normed space, \(f\) and \(g\) are upper semicontinuous, with nonempty closed convex values, \(f-g\) is weakly inward, and on this domain \(Y\) of \(F\) there is considered an appropriate Hausdorff metric \(\rho\). The main result asserts, for each \(y\in Y\), there exists a connected component of \(F(y)\) which is an essential one, that is, for each open set \(O\supseteq F(y)\), there exists \(\delta>0\) such that \(F(y')\cap O\neq\emptyset\) for all \(y'\in Y\) with \(\rho(y',y)<\delta\).
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47H04
zbMATH DE Number: 1369360
zbMATH Keywords: coincident points
zbMATH Keywords: set-valued mappings
zbMATH Keywords: weakly inward
zbMATH Keywords: Hausdorff metric
reviewed by: Corneliu Ursescu
MaRDI profile type: Publication
cites work: Q5812718
cites work: On essential components of the set of Nash equilibrium points
cites work: The stability of coincident points for multivalued mappings
cites work: Q3220809
cites work: Fixed point and coincidence theorems of set-valued mappings in topological vector spaces with some applications
description: scientific article; zbMATH DE number 1369360