The Relationship between Two Kinds of Generalized Convex Set-Valued Maps in Real Ordered Linear Spaces

Abstract EN

A new notion of the ic-cone convexlike set-valued map characterized by the algebraic interior and the vector closure is introduced in real ordered linear spaces.

The relationship between the ic-cone convexlike set-valued map and the nearly cone subconvexlike set-valued map is established.

The results in this paper generalize some known results in the literature from locally convex spaces to linear spaces.