Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce the concept of $\beta$-preconvex sets on preconvexity spaces. We study some properties for $\beta$-preconvex sets by using the co-convexity hull and the convexity hull. Also we introduce and study the concepts of $\beta c$-convex function and $\beta ^* c$-convex function.

Keywords: preconvexity, co-convex sets, convexity, $\beta^* c$-convex function, $\beta c$-convex function, co$\beta$-preconvex sets, $\beta$-preconvex sets

MSC numbers: Primary 52A01