The generalized vector quasi-variational-like inequalities
type: Item
instance of: scholarly article
title: The generalized vector quasi-variational-like inequalities
zbMATH Open document ID: 0944.47040
DOI: 10.1016/S0898-1221(99)00076-0
publication date: 2000-01-20T00:00:00Z
review text: The following class of generalized vector quasi-variational-like inequalities in real Hausdorff topological spaces \(E,\;F\) is studied: \(\widetilde x \in G(\widetilde x)\), for any \(y \in G(\widetilde x)\) there is \(\widetilde u \in T(\widetilde x)\) such that \((\widetilde u,\eta(y,\widetilde x)) \notin -\operatorname {int} C(\widetilde x).\) Here \(T:X \to 2^{L(E,F)}\), \(G:X \to 2^X\), \(C:X \to 2^F\) are set-valued mappings (\(X\) is a nonempty convex subset of \(E\)), \(\eta:X\times X \to E\) is a single-valued mapping. It is supposed that \(C(x)\) is a closed convex cone, \(C(x) \cap -C(x) = \{\emptyset \}\)), \(\operatorname {int} C(x)\neq \emptyset\) for any \(x \in X\), \(G\) is hemicontinuous with compact values, \(T\) satisfies a certain monotonicity assumption. Some particular cases are mentioned. General existence results are established by using a scalarization technique.
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 1391536
zbMATH Keywords: generalized vector quasi-variational-like inequality
zbMATH Keywords: \(C_+\eta\)-monotone
zbMATH Keywords: topological vector space
zbMATH Keywords: set-valued mappings
zbMATH Keywords: hemicontinuous with compact values
zbMATH Keywords: monotonicity
zbMATH Keywords: scalarization technique
author: Xieping Ding
reviewed by: Milan Kučera
MaRDI profile type: Publication
cites work: Q3944358
cites work: Existence of solutions for a vector variational inequality: An extension of the Hartmann-Stampacchia theorem
cites work: The vector complementary problem and its equivalences with the weak minimal element in ordered spaces
cites work: Q3468900
cites work: A vector variational inequality and optimization over an efficient set
cites work: On vector variational inequalities
cites work: Vector complementarity and minimal element problems
cites work: Vector variational inequality and its duality
cites work: Generalized convex functions and vector variational inequalities
cites work: Generalized vector variational inequality and fuzzy extension
cites work: Generalized vector variational inequality
cites work: Generalized vector variational inequalities
cites work: On the generalized vector variational inequality problem
cites work: Existence theorems for vector variational inequalities
cites work: Existence of solutions for a generalized vector quasivariational inequality
cites work: On vector quasivariational inequalities
cites work: A Note On Generalized Vector Variational-Like Inequalities
cites work: Q4351544
cites work: Q5620935
cites work: Generalized quasivariational inequalities in locally convex topological vector spaces
cites work: Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities
cites work: The Generalized Quasi-Variational Inequality Problem
cites work: Generalized variational inequalities and generalized quasi-variational inequalities
cites work: Existence of solutions for generalized quasi-variational-like inequalities
cites work: Generalized variational-like inequalities with nonmonotone set-valued mappings
cites work: Generalized quasi-variational inequalities and some applications
cites work: Q4344972
cites work: Quasi-variational inequalities and social equilibrium
cites work: Q5809478
cites work: Q5185568
full work available at URL: s0898-1221(99)00076-0
OpenAlex ID: W2081007166
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1391536