Midconvexity for finite sets

作者：Tabor Jacek; Tabor Jozef; Misztal Krzysztof^*

来源：Journal of Inequalities and Applications, 2013, 2013(1): 42.

DOI：10.1186/1029-242X-2013-42

• midconvex set
• midconvex function
• midconvex hull

Let X be a finite subset of a real vector space. We study Jensen-type convexity on subsets of X. In particular for subsets of X, we introduce the definition of X-midconvex sets. We show that such a notion corresponds well to the classical notion of a convex set. Moreover, we prove that a function X-midconvex set is a midconvex hull of all its extremal points. Other analogues of some classical results are also given. At the end we present an algorithmic approach to finding the midconvex hull of a given set.

• 出版日期2013