A theorem of the Hahn-Banach type and its applications
Annales Polonici Mathematici, Tome 57 (1992) no. 3, pp. 243-252
Let Y be a subgroup of an abelian group X and let T be a given collection of subsets of a linear space E over the rationals. Moreover, suppose that F is a subadditive set-valued function defined on X with values in T. We establish some conditions under which every additive selection of the restriction of F to Y can be extended to an additive selection of F. We also present some applications of results of this type to the stability of functional equations.
Keywords:
Hahn-Banach theorem, additive selection, subadditive set-valued function, binary intersection property, stability of functional equations
@article{10_4064_ap_57_3_243_252,
author = {Zbigniew Gajda and Andrzej Smajdor and Wilhelmina Smajdor},
title = {A theorem of the {Hahn-Banach} type and its applications},
journal = {Annales Polonici Mathematici},
pages = {243--252},
year = {1992},
volume = {57},
number = {3},
doi = {10.4064/ap-57-3-243-252},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-57-3-243-252/}
}
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Zbigniew Gajda; Andrzej Smajdor; Wilhelmina Smajdor. A theorem of the Hahn-Banach type and its applications. Annales Polonici Mathematici, Tome 57 (1992) no. 3, pp. 243-252. doi: 10.4064/ap-57-3-243-252
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