Lower Semicontinuity Of Efficient Solution Mapping For Parameter Vector Optimization Problems And Henig Approximate Duality For Vector Quasi-equilibrium Problems

In the first part of this paper,, we obtain scalarization results of Henig efficient solution mapping, global efficient solution mapping, super-efficient solution mapping and cone-Benson efficient solution mapping of parametric vector optimization problems in locally convex topological vector spaces. We study lower semicontinuity of efficient solution mapping, global efficient solution mapping, super-efficient solution mapping and cone-Benson efficient solution mapping of parametric vector optimization problems by using scalarization results.In the second part, without the generalized Slater condition, we discuss the relationship between ε-Henig efficient solution of the ε-Henig vector quasi-equilibrium problem and ε-Henig efficient solution of its duality problem by using the concept of quasi interior of convex sets and we get the duality theorem of the vector quasi-equilibrium problem.