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ArticleOriginal scientific text

Title

A selection theorem of Helly type and its applications

Authors 1, 2

Affiliations

  1. Freie Universität Berlin, I Mathematisches Institut, Arnimallee 3, 14195 Berlin, Germany
  2. Department Of Mathematics, Łódź Technical University, Bielsko-Biała Branch, Willowa 2, 43-309 Bielsko-Biała, Poland

Abstract

We prove an abstract selection theorem for set-valued mappings with compact convex values in a normed space. Some special cases of this result as well as its applications to separation theory and Hyers-Ulam stability of affine functions are also given.

Bibliography

  1. K. Baron, J. Matkowski and K. Nikodem, A sandwich with convexity, Math. Pannonica 5 (1994), 139-144.
  2. D. H. Hyers and S. M. Ulam, Approximately convex functions, Proc. Amer. Math. Soc. 3 (1952), 821-828.
  3. K. Nikodem and S. Wąsowicz, A sandwich theorem and Hyers-Ulam stability of affine functions, Aequationes Math., to appear.
  4. F. A. Valentine, Convex Sets, McGraw-Hill, New York, 1964.
  5. S. Wasowicz, On affine selections of set-valued functions, to appear.
Studia Mathematica
1995/116/1
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Pages:
43-48
Main language of publication
English
Received
1994-09-13
Accepted
1995-03-01
Published
1995
Exact and natural sciences