On existence of a solution for the system of generalized vector quasi-equilibrium problems with upper semicontinuous set-valued maps

On existence of a solution for the system of generalized vector quasi-equilibrium problems with upper semicontinuous set-valued maps

Throughout this paper, we use intA and CoA to denote the interior and the convex hull of a set A, respectively. Let I be an index set. For each i ∈ I , let Yi, Ei be two Hausdorff topological vector spaces. Consider a family of nonempty convex subsets {Xi}i∈I with Xi ⊆ Ei. Let X = ∏ i∈I Xi and E = ∏ i∈I Ei. An element of the set Xi = ∏ j∈I\i Xi will be denoted by xi; therefore, x ∈ X will be wr...

Some existence results for generalized vector quasi-equilibrium problems

‎In this paper‎, ‎we introduce and study a class of generalized vector quasi-equilibrium problem‎, ‎which includes many vector equilibrium problems‎, ‎equilibrium problems‎, ‎vector variational inequalities and variational inequalities as special cases‎. ‎Using one person game theorems‎, ‎the concept of escaping sequences and without convexity assumptions‎, ‎we prove some existence results for ...

Gap functions for a system of generalized vector quasi-equilibrium problems with set-valued mappings

Throughout this paper, let Z, E, and F be topological vector spaces, let X ⊆ E and Y ⊆ F be nonempty, closed, and convex subsets. Let D : X → 2X , T : X → 2Y and Ψ : X ×Y × X → 2Z be set-valued mappings, and let C : X → 2Z be a set-valued mapping such that C(x) is a closed pointed and convex cone with intC(x) = ∅ for each x ∈ X , where intC(x) denotes the interior of the set C(x). Then the gene...

some existence results for generalized vector quasi-equilibrium problems

‎in this paper‎, ‎we introduce and study a class of generalized vector quasi-equilibrium problem‎, ‎which includes many vector equilibrium problems‎, ‎equilibrium problems‎, ‎vector variational inequalities and variational inequalities as special cases‎. ‎using one person game theorems‎, ‎the concept of escaping sequences and without convexity assumptions‎, ‎we prove some existence results for ...

Parametric Set-Valued Vector Quasi-Equilibrium Problems