In this paper we establish sufficient conditions for the solution set of parametric multivalued vector quasiequilibrium problems to be semicontinuous. All kinds of semicontinuity are considered: lower semicontinuity, upper semicontinuity, Hausdorff upper semicontinuity and closedness. Moreover, we investigate both the "weak" and "strong" solutions of quasiequilibrium problems.  2004 Elsevier Inc. All rights reserved.

Locally convex spaces, Weak τ-functions, Ekeland’s variational principle, K-lower semicontinity from above, Lower closedness,

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We consider parametric multivalued vector equilibrium problems of both weak and strong types in metric linear spaces. Sufficient conditions for the local uniqueness and Hölder continuity of the solutions are established. As consequences some new results for variational inequalities are derived and compared with recent papers on the subject.