Vector variational-type inequalities for set-valued mappings
type: Item
instance of: scholarly article
title: Vector variational-type inequalities for set-valued mappings
zbMATH Open document ID: 0977.47056
DOI: 10.1016/S0893-9659(99)00186-X
author: Byung-Soo Lee
author: Suk-Jin Lee
published in: Applied Mathematics Letters
publication date: 2000-12-04T00:00:00Z
review text: This article deals with the generalized vector variational-type inequality problem of finding \(x_0\in K\) such that for all \(y\in K\) there exists \(s_0\in T(x_0)\) for which \[ \langle s_0, \theta(y, x_0)\rangle+ \eta(x_0, y)\not\in- \text{int }C(x_0), \] where \(K\) is a nonempty convex subset of a Hausdorff topological vector space \(X\), \(Y\) a topological vector space, \(T: K\to 2^{L(X, Y)}\), \(\theta: K\to X\), \(\eta: K\times K\to Y\) (\(L(X, Y)\) is the space of all continuous linear operators between \(X\) and \(Y\)), \(\{C(x): x\in K\}\) a family of closed convex cones in \(Y\). The main results are two theorems on solvability of the problem under considerations.
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1540356
zbMATH Keywords: generalized vector variational-type inequality problem
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1540356