Weighted variational inequalities
type: Item
instance of: scholarly article
title: Weighted variational inequalities
zbMATH Open document ID: 1108.49004
published in: Journal of Optimization Theory and Applications
publication date: 2006-11-06T00:00:00Z
review text: From the authors' summary: In this paper, we introduce weighted variational inequalities over product of sets and system of weighted variational inequalities. It is noted that the weighted variational inequality problem over product of sets and the problem of system of weighted variational inequalities are equivalent. We give a relationship between system of weighted variational inequalities and systems of vector variational inequalities. We define several kinds of weighted monotonicities and establish several existence results for the solution of the above-mentioned problems under these weighted monotonicities. We introduce also the weighted generalized variational inequalities over product of sets, that is, weighted variational inequalities for multivalued maps and systems of weighted generalized variational inequalities. Extensions of weighted monotonicities for multivalued maps are also considered. The existence of a solution of weighted generalized variational inequalities over product of sets is also studied. The existence results for a solution of weighted generalized variational inequality problem give also the existence of solutions of systems of generalized vector variational inequalities.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 5070988
zbMATH Keywords: Weighted variational inequalities
zbMATH Keywords: system of vector variational inequalities
zbMATH Keywords: weighted generalized variational inequalities
zbMATH Keywords: system of generalized vector variational inequalities
zbMATH Keywords: Nash equilibrium problems
author: Qamrul Hasan Ansari
author: Zubair Khan
author: A. H. Siddiqi
reviewed by: Hans Benker
MaRDI profile type: Publication
full work available at URL: s10957-005-6539-4
OpenAlex ID: W2082215958
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DOI: 10.1007/S10957-005-6539-4
description: scientific article; zbMATH DE number 5070988