A selection theorem of Helly type and its applications

Ehrhard Behrends; Kazimierz Nikodem

Studia Mathematica (1995)

  • Volume: 116, Issue: 1, page 43-48
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Behrends, Ehrhard, and Nikodem, Kazimierz. "A selection theorem of Helly type and its applications." Studia Mathematica 116.1 (1995): 43-48. <http://eudml.org/doc/216218>.

@article{Behrends1995,
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.},
author = {Behrends, Ehrhard, Nikodem, Kazimierz},
journal = {Studia Mathematica},
keywords = {Helly-type abstract selection theorem; set-valued mappings; normed space; affine functions},
language = {eng},
number = {1},
pages = {43-48},
title = {A selection theorem of Helly type and its applications},
url = {http://eudml.org/doc/216218},
volume = {116},
year = {1995},
}

TY - JOUR
AU - Behrends, Ehrhard
AU - Nikodem, Kazimierz
TI - A selection theorem of Helly type and its applications
JO - Studia Mathematica
PY - 1995
VL - 116
IS - 1
SP - 43
EP - 48
AB - 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.
LA - eng
KW - Helly-type abstract selection theorem; set-valued mappings; normed space; affine functions
UR - http://eudml.org/doc/216218
ER -

References

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  1. [1] K. Baron, J. Matkowski and K. Nikodem, A sandwich with convexity, Math. Pannonica 5 (1994), 139-144. Zbl0803.39011
  2. [2] D. H. Hyers and S. M. Ulam, Approximately convex functions, Proc. Amer. Math. Soc. 3 (1952), 821-828. Zbl0047.29505
  3. [3] K. Nikodem and S. Wąsowicz, A sandwich theorem and Hyers-Ulam stability of affine functions, Aequationes Math., to appear. Zbl0815.39010
  4. [4] F. A. Valentine, Convex Sets, McGraw-Hill, New York, 1964. 
  5. [5] S. Wasowicz, On affine selections of set-valued functions, to appear. Zbl0887.26007

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