Wellposedness for a class of strong vector equilibrium problems

In this paper, we first construct a complete metric space Lambda consisting of a class of strong vector equilibrium problems (for short, (SVEP)) satisfying some conditions. Under the abstract framework, we introduce a notion of wellposedness for the (SVEP), which unifies its Hadamard and Tikhonov wellposedness. Furthermore, we prove that there exists a dense (G_delta set Q of Lambda such that each (SVEP) in Q is wellposed, that is, the majority (in Baire category sense) of (SVEP) in Lambda is wellposed. Finally, metric characterizations on the wellposedness for the (SVEP) are given.