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.
@article{bwmeta1.element.bwnjournal-article-smv116i1p43bwm,
author = {Ehrhard Behrends and Kazimierz Nikodem},
title = {A selection theorem of Helly type and its applications},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {43-48},
zbl = {0847.52004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv116i1p43bwm}
}
Behrends, Ehrhard; Nikodem, Kazimierz. A selection theorem of Helly type and its applications. Studia Mathematica, Tome 113 (1995) pp. 43-48. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv116i1p43bwm/
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