Semi-preconvex sets on preconvexity spaces
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.
Keywords : preconvexity, co-convex sets, convexity, $s^* c$-convex function, $sc$-convex function, cosemi-preconvex sets, semi-preconvex sets
MSC numbers : 52A01
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