Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce the concept of the semi-preconvex set on preconvexity spaces. We study some properties for the semi-preconvex set. Also we introduce the concepts of the $sc$-convex function and $s^* c$-convex function. Finally, we characterize $sc$-convex functions, $s^*$-convex functions and semi-preconvex sets by using the co-convexity hull and the convexity hull.

Keywords: preconvexity, co-convex sets, convexity, $s^* c$-convex function, $sc$-convex function, cosemi-preconvex sets, semi-preconvex sets

MSC numbers: 52A01