Variational inequalities and surjectivity for set-valued monotone mappings
type: Item
instance of: scholarly article
title: Variational inequalities and surjectivity for set-valued monotone mappings
zbMATH Open document ID: 0989.49009
DOI: 10.12775/TMNA.1998.035
author: K. Appert
published in: Topological Methods in Nonlinear Analysis
publication date: 2002-07-09T00:00:00Z
review text: The authors establish an existence theorem for a variational inequality of the type: Find \((y,w)\) in the graph of \(T\) such that \(\text{Re}\langle w,x-y\rangle\) is nonnegative for all \(x\) in \(X\). \(X\) is a convex set, and \(T\) is a monotone multivalued mapping. Appropriate compactness conditions are also assumed. The existence result is proved with the help of a standard KKM theorem. As an application, the authors provide a surjectivity criterion for the multivalued mapping \(T\).
reviewed by: Alberto Seeger
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 47J20
zbMATH DE Number: 1279192
zbMATH Keywords: variational inequality
zbMATH Keywords: monotone operator
MaRDI profile type: Publication
full work available at URL: tmna.1998.035
OpenAlex ID: W2574433971
description: scientific article; zbMATH DE number 1279192