An existence result for the generalized vector equilibrium problem
type: Item
instance of: scholarly article
title: An existence result for the generalized vector equilibrium problem
zbMATH Open document ID: 1014.49008
DOI: 10.1016/S0893-9659(99)00121-4
author: Jen-Chih Yao
author: Qamrul Hasan Ansari
published in: Applied Mathematics Letters
publication date: 2003-07-22T00:00:00Z
review text: Let \(X\) and \(Y\) be two topological vector spaces, \(K\) a nonempty convex subset of \(X\), and \(F : K \times K \to 2^Y\) a multifunction. Let \(C : K\to 2^Y\) be a multifunction such that for each \(x\in K\), \(C(x)\) is a closed convex cone with \(\text{int }C(x)\neq 0\), where \(\text{int } C(x)\) denotes the interior of \(C(x)\). Then, the authors consider the following generalized vector equilibrium problem which consists of finding \[ F(\overline x, y)\nsubseteq -\text{int }C(\overline x)\quad \text{for all } y\in K. \] By using the Fan-Browder type fixed-point theorem due to \textit{E. Tarafdar} [J. Math. Anal. Appl. 128, 475-479 (1987; Zbl 0644.47050)], they present an existence result for the above problem, extending the result in \textit{E. Tarafdar} and \textit{G. X.-Z. Yuan} [Nonlinear Anal., Theory Methods Appl. 30, No.~7, 4171-4181 (1997; Zbl 0912.49004)]. It is very interesting for us.
reviewed by: J. K. Kim
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 49J53
zbMATH DE Number: 1428528
zbMATH Keywords: multifunction
zbMATH Keywords: generalized vector equilibrium problem
zbMATH Keywords: fixed-point
MaRDI profile type: Publication
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full work available at URL: s0893-9659(99)00121-4
OpenAlex ID: W2159553266
description: scientific article; zbMATH DE number 1428528