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Existence theorems for vector variational inequalities

Published online by Cambridge University Press:  17 April 2009

Aris Daniilidis  and
Nicolas Hadjisavvas
Aris Daniilidis
Affiliation:
Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece, e-mail: [email protected], [email protected]
Nicolas Hadjisavvas
Affiliation:
Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece, e-mail: [email protected], [email protected]
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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 x0 ∈ K such that for every x ∈ K we have A(x − x0) ∉ − int C for some A ∈ Tx0. These results correct previously published ones.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 473 - 481
Copyright
Copyright © Australian Mathematical Society 1996

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