The system of generalized set-valued equilibrium problems

The System of Generalized Set-valued Equilibrium Problems

We introduce new and interesting model of system of generalized set-valued equilibrium problems which generalizes and unifies the system of set-valued equilibrium problems, the system of generalized implicit vector variational inequalities, the system of generalized vector and vector-like variational inequalities introduced by Ansari et al. (2002), the system of generalized vector variational i...

Lower semicontinuity for parametric set-valued vector equilibrium-like problems

A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...

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...

Parametric Set-Valued Vector Quasi-Equilibrium Problems

lower semicontinuity for parametric set-valued vector equilibrium-like problems

a concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $k$...