Abstract
In this paper, we provide the connectedness of the sets of weak efficient solutions, Henig efficient solutions and Benson proper efficient solutions for set-valued vector equilibrium problems under improvement sets.
Highlights
In recent years, many scholars paid attention to developing concepts to unify various kinds of solution notions of vector optimization problems, for instance, efficiency, weak efficiency, proper efficiency and ε-efficiency
Motivated by the work of [13, 24, 25], in this paper, by using the scalarization results, we study the connectedness of the sets of weakly efficient solutions, Henig efficient solutions and Benson proper efficient solutions for set-valued vector equilibrium problems under improvement sets
5 Conclusions In this paper, under the assumption of nearly E-subconvexlikeness of the binary function in real locally convex Hausdorff topological vector spaces, we obtain the linear scalarization of weak efficient solutions, Benson proper efficient solutions, Heing efficient solutions for (USVEP)
Summary
Many scholars paid attention to developing concepts to unify various kinds of solution notions of vector optimization problems, for instance, efficiency, weak efficiency, proper efficiency and ε-efficiency. Let B be a base of C, because of 0Y ∈/ cl B, by the separation theorem of convex sets, there exists 0 = φ ∈ Y ∗ such that δ = inf φ(b) | b ∈ B > φ(0Y ) = 0. The set-valued map F : A ⇒ Y is said to be nearly E-subconvexlike on A if cl(cone(F(A) + E)) is a convex set in Y .
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