Abstract
AbstractIn this paper, a scalarization result of ε-weak efficient solution for a vector equilibrium problem (VEP) is given. Using this scalarization result, the connectedness of ε-weak efficient and ε-efficient solutions sets for the VEPs are proved under some suitable conditions in real Hausdorff topological vector spaces. The main results presented in this paper improve and generalize some known results in the literature.
Highlights
1 Introduction Let K be a nonempty subset of a real Hausdorff topological vector space E, and f : K × K ® R a bifunction such that f(x, x) ≥ 0 for all x Î K
The scalar equilibrium problem consists in finding x ∈ K such that f (x, y) ≥ 0, ∀y ∈ K. It provides a unifying framework for many important problems, such as optimization problems, variational inequality problems, complementary problems, minimax inequality problems, Nash equilibrium problems, and fixed point problems, and has been widely applied to study problems arising in economics, mechanics, and engineering science
It is well known that another important problem for vector equilibrium problem (VEP) is to study the topological properties of solutions set
Summary
Let K be a nonempty subset of a real Hausdorff topological vector space E, and f : K × K ® R a bifunction such that f(x, x) ≥ 0 for all x Î K. It is well known that another important problem for VEPs is to study the topological properties of solutions set. We discuss the connectedness of ε-weak efficient and ε-efficient solutions sets for VEPs under some suitable conditions in real Hausdorff topological vector spaces.
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