Commun. Korean Math. Soc. 2008 Vol. 23, No. 2, 251-256 Printed June 1, 2008
Won Keun Min Kangwon National University
Abstract : 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.