• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.251-256
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• 2008

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.