Bulletin of the Australian Mathematical Society

Research Article

Existence theorems for vector variational inequalities

Aris Daniilidisa1 and Nicolas Hadjisavvasa1

a1 Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece, e-mail: arisd@kerkis.math.aegean.gr, nhad@kerkis.math.aegean.gr

Abstract

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 xs2208 K such that for every x xs2208 K we have A(xx0) xs2209 − int C for some A xs2208 Tx0. These results correct previously published ones.

(Received January 04 1996)