Existence of Solutions to Generalized Vector Quasi–Equilibrium Problems with Discontinuous Mappings.

Let X, Y be two finite–dimensional topological vector spaces, Z a Hausdorff topological vector space, K ⊂ X and D ⊂ Z be two nonempty sets, C be a pointed, closed, and convex cone in Y with int C ≠ Ø. Let S : K → 2 K and T : K → 2 D be two multivalued mappings, and φ : K× D× K → Y be a trifunction. In this paper, we consider the generalized vector quasi–equilibrium problem, which is formulated by finding $\hat x$ ∈ K and ŷ ∈ T( $\hat x$ ) such that $\hat x$ ∈ S( $\hat x$ ) and φ( $\hat x$ , ŷ, u) /∈ −int C for all u ∈ S( $\hat x$ ). We establish an existence result in which T is not supposed to have any continuity property. Our results extend and improve the corresponding results of Cubiotti, Yao and Guo. [ABSTRACT FROM AUTHOR]