Variational inequality problem in Hausdorff topological vector spaces
type: Item
instance of: scholarly article
title: Variational inequality problem in Hausdorff topological vector spaces
zbMATH Open document ID: 0879.49009
author: G. K. Panda
author: Akrur Behera
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1998-01-25T00:00:00Z
review text: The authors considered the generalized variational type inequality problem: Find \(\overline x\in K\), such that \[ \langle T(\overline x),g(y,\overline x)\rangle\geq 0\quad\text{for all }\overline x\in K, \] where \(K\) is a nonempty convex subset of a Hausdorff topological space \(X\) with dual space \(X^*\), \(T:K\to X^*\), \(G:K\times K\to X\). They use a KKM theorem of Fan to establish existence theorems of the above inequality. If \(g(y,x)= y-f(x)\), where \(f:K\to K\) is a continuous function, then the problem reduces to the case considered by Isac.
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1013750
zbMATH Keywords: monotone operator
zbMATH Keywords: hemicontinuous operator
zbMATH Keywords: variational inequality
zbMATH Keywords: KKM theorem
reviewed by: Lai-Jiu Lin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1013750