A variational principle for vector equilibrium problems
type: Item
instance of: scholarly article
title: A variational principle for vector equilibrium problems
zbMATH Open document ID: 1019.49017
DOI: 10.1007/BF02829618
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2003-09-05T00:00:00Z
review text: The author describes a variational principle for vector equilibrium problems of finding \(x\in K\) such that \[ f(x,y)\not\in -\text{int }P \] for all \(y\in K\), where \(\text{ int}P\) denotes the topological interior of the cone \(P\), \(X\) is a real topological vector space, \(K\) is a nonempty closed convex subset of \(X\), \((Y,P)\) is a real ordered topological vector space, and \(f:X\times X\to Y\) is a mapping with \(f(x,x)=0\) for all \(x\in X\). Under some conditions, the author analyses the solutions for vector equilibrium problems and obtains some new results.
reviewed by: Nan-Jing Huang
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 91B52
zbMATH DE Number: 1740620
zbMATH Keywords: vector equilibrium problem
zbMATH Keywords: variational principle
zbMATH Keywords: \(P\)-convexity
zbMATH Keywords: \(P\)-\(\psi\)-monotonicity
author: K. R. Kazmi
MaRDI profile type: Publication
cites work: Variational principles for variational inequalities
cites work: Q4863208
cites work: Q4366516
cites work: Existence of solutions for a vector variational inequality: An extension of the Hartmann-Stampacchia theorem
cites work: Existence and continuity of solutions for vector optimization
cites work: Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
cites work: Some remarks on vector optimization problems
cites work: On vector equilibrium problem
cites work: Q4762227
cites work: Vector complementarity and minimal element problems
description: scientific article; zbMATH DE number 1740620