Existence theorems of solutions for a kind of quasi-variational inequalities with monotone type multivalued mapping
type: Item
instance of: scholarly article
title: Existence theorems of solutions for a kind of quasi-variational inequalities with monotone type multivalued mapping
zbMATH Open document ID: 0939.47056
DOI: 10.1016/S0898-1221(99)00132-7
author: Xian Wu
publication date: 2000-01-20T00:00:00Z
review text: Let \(X\) be a topological space and \(\{F_A\}\) be a family of nonempty contractible subsets of \(X\) indexed by a nonempty finite subset \(A\) of \(X\). The pair \((X,\{F_A\})\) is called an \(H\)-space. Let \(Y\) be a topological space, \(\varphi: X\times Y\times X\to R\) and \(T: X\to 2^Y\) be a \(\varphi\)-monotone multivalued mapping with nonempty values. The main results of this paper are two existence theorems for the following quasivariational inequality: find \(u_0\in X\) such that \(\sup\{\varphi(v,w,u_0): w\in T(u_0)\}\geq 0\), for all \(v\in X\).
reviewed by: Adrian Petruşel
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1391571
zbMATH Keywords: transfer open valued multifunction
zbMATH Keywords: \(H\)-space
zbMATH Keywords: \(\varphi\)-monotone multivalued mapping
zbMATH Keywords: existence theorems
zbMATH Keywords: quasivariational inequality
MaRDI profile type: Publication
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full work available at URL: s0898-1221(99)00132-7
OpenAlex ID: W2040748217
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1391571