On affine selections of set-valued functions

Sz. Wasowicz

Abstract: The main result of this paper is the theorem stating that every convex set--valued function $F:I\mapsto c(Y)$, where $I\subset {\bf R}$ is an interval and $Y$ is a locally convex space, possesses an affine selection. In the case if $Y={\bf R}$ and values of $F$ are closed real intervals we can replace the assumption of convexity of $F$ by the more general condition.

Keywords: Set-valued functions, selections, convex (concave) set-valued functions, affine functions,locally convex spaces

Classification (MSC2000): 26E25; 54C65

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