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.
słowa kluczowe w j. angielskim:
midconvex set, midconvex function, midconvex hull
liczba arkuszy wydawniczych:
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wydział: instytut / zakład / katedra:
Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej