Closedness of the Solution Map for Parametric Vector Equilibrium Problems with Trifunctions
نویسندگان
چکیده
Bogdan and Kolumbán [3] gave sufficient conditions for closedness of the solution map defined on the set of parameters. They considered the parametric equilibrium problems governed by topological pseudomonotone maps depending on a parameter. In this paper we generalize this result for parametric vector equilibrium problems with trifunctions. Let X and Y be Hausdorff topological spaces and P , the set of parameters, another Hausdorff topological space, T : X → 2Y be a multi-valued mapping. Generalized vector equilibrium problems (GV EP for short) are obtained from generalized equilibrium problems by considering trifunctions on K×D× K into a real topological vector space Z with an ordering cone. By an ordering cone C ⊂ Z we mean that C is a closed convex cone in Z with IntC 6= ∅ and C 6= Z, where IntC denotes the interior of C. Let fp : X×Y ×X → Z be a trifunction. For a given p ∈ P , we consider the following problem (GV EP )p: Find a pair (xp, yp) ∈ Kp × T (xp) such that fp (xp, yp, u) ∈ (− IntC) for all u ∈ Kp,
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