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Existence theorems for vector variational inequalities

Published online by Cambridge University Press:  17 April 2009

Aris Daniilidis
Affiliation:
Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece, e-mail: arisd@kerkis.math.aegean.gr, nhad@kerkis.math.aegean.gr
Nicolas Hadjisavvas
Affiliation:
Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece, e-mail: arisd@kerkis.math.aegean.gr, nhad@kerkis.math.aegean.gr
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Abstract

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Given two real Banach spaces X and Y, a closed convex subset K in X, a cone with nonempty interior C in Y and a multivalued operator from K to 2L(x, y), we prove theorems concerning the existence of solutions for the corresponding vector variational inequality problem, that is the existence of some x0K such that for every xK we have A(xx0) ∉ − int C for some ATx0. These results correct previously published ones.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1996

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