We prove that strictly efficient points are indeed equivalent to Henig proper efficient points.

By this concept, we give a few results on Chebyshev scalaxization of a Henig efficient point.

We establish a scalarization theorem,a Lagrange multiplier theorem and duality theorem for Henig proper efficiency with respect to a base in vector optimization problem involving nearly subconvexlike set-valued maps in locally convex topological vector spaces.

In this paper, we study Henig proper efficiency with respect to a base for vector optimization problem involving nearly subconvexlike set-valued maps in the framework of locally convex topological vector spaces.