Remarks on implicit vector variational inequalities.
type: Item
instance of: scholarly article
title: Remarks on implicit vector variational inequalities.
zbMATH Open document ID: 1035.49005
author: Sangho Kum
author: Gue Myung Lee
published in: Taiwanese Journal of Mathematics
publication date: 2002-01-01T00:00:00Z
review text: In this paper, the authors consider two implicit vector variational inequalities. One is proposed and studied by the authors in [J. Optimization Theory Appl. 104, 409--425 (2000; Zbl 0970.47052)] and the other one is the generalized form of the previous one. They generalize the concepts of pseudomonotonicity and hemicontinuity which are earlier studied in [loc. cit]. By adopting the technique developed there the existence of solutions of these two implicit vector variational inequalities is studied. The strong solutions of these two inequalities are also studied by using the scalarization method of \textit{I.V. Konnov} and \textit{J. C. Yao} [J. Math. Anal. Appl. 206, 42-58 (1997; Zbl 0878.49006)] and by using a continuous selection theorem.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 49J53
zbMATH DE Number: 1876791
zbMATH Keywords: vector variational inequalities
zbMATH Keywords: pseudomonotone maps
zbMATH Keywords: hemicontinuous map
zbMATH Keywords: Fan-Browder fixed-point theorem
zbMATH Keywords: selection theorem
reviewed by: Qamrul Hasan Ansari
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500558302
OpenAlex ID: W1497178110
DOI: 10.11650/TWJM/1500558302
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description: scientific article; zbMATH DE number 1876791