EMIS ELibM Electronic Journals Journal of Applied Analysis
Vol. 1, No. 2, pp. 173-179 (1995)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



On affine selections of set-valued functions

Sz. Wasowicz

Department of Mathematics
Technical University of Lodz
Branch in Bielsko-Biala
ul. Willowa 2
43-309 Bielsko-Biala, Poland
e-mail: szw@merc.pb.bielsko.pl

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

Full text of the article:

Electronic fulltext finalized on: 29 May 2002. This page was last modified: 21 Dec 2002.

© 2002 Heldermann Verlag
© 2002 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition