Continuity properties of midconvex set-valued maps

被引：0

作者：

Nikodem K. ^{[1
]}

机构：

[1] Department of Mathematics, Technical University of Łódź, Branch in Bielsko-Biała, PL-43-309 Bielsko-Biała

来源：

aequationes mathematicae | 2001年 / 62卷 / 1期

关键词：

Additive functions; Convex functions; K-continuity; K-midconvex set-valued maps; Set-valued maps;

D O I：

10.1007/PL00000137

中图分类号：

学科分类号：

摘要：

Some new results on the continuity of K-midconvex set-valued maps are given. In particular it is shown that (under suitable assumptions on D, Y and K) a K-midconvex set-valued map F : D → cc(Y) is K-continuous if and only if for every linear continuous positive functional y* : Y → ℝ the functional fy*(x) = inf y* (F(x)), x ∈ D, is continuous. As a consequence of this result we obtain the equality of some set-classes connected with additive functionals and K-midconvex set-valued maps. © Birkhäuser Verlag, Basel, 2001.

引用

页码：175 / 183

页数：8

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