Variational inequalities with operator solutions
type: Item
instance of: scholarly article
title: Variational inequalities with operator solutions
zbMATH Open document ID: 1009.47064
DOI: 10.1023/A:1014096127736
published in: Journal of Global Optimization
publication date: 2002-05-28T00:00:00Z
review text: The authors consider the following operator variational inequality (OVI) problem: find \(f_0\in K\) such that \(\langle f-f_0,T(f_0)\rangle\notin C(f_0),\) for every \(f\in K,\) where \(X,Y\) are Hausdorff topological vector spaces, \((X,Y)^*\) denotes the space of linear and continuous operators from \(X\) into \(Y\), \(K\subset (X,Y)^*\) is a nonempty, convex set, \(T:K\to X\) is a mapping and \(C:K\to 2^Y\) is a set-valued mapping with convex, cone values such that \(0\notin C(f)\) for all \(f\in K.\) The authors study the solvability of the problem (OVI) using the \(C\)-pseudomonotonicity assumption, improving a previous result by Yu and Yao. As a particular case of (OVI) the authors study the solvability of scalar variational inequalities on Hausdorff topological vector spaces. Finally, they generalize the notion of pseudomonotonicity introduced by Brézis defining the \(B\)-pseudomonotonicity and prove, under this assumption, the solvability of (OVI).
reviewed by: Rita Pini
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 49J53
zbMATH DE Number: 1746313
zbMATH Keywords: variational inequalities
zbMATH Keywords: pseudomonotonicity
zbMATH Keywords: KKM-mapping
author: András Domokos
author: J. Kolumbán
MaRDI profile type: Publication
full work available at URL: a:1014096127736
OpenAlex ID: W1496528026
description: scientific article; zbMATH DE number 1746313