ArticleOriginal scientific text
Title
A theorem of the Hahn-Banach type and its applications
Authors 1, 2, 1
Affiliations
- Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
- Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland
Abstract
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
Bibliography
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- K. Baron, Functions with differences in subspaces, in: Proceedings of the 18th International Symposium on Functional Equations, University of Waterloo, Faculty of Mathematics, Waterloo, Ont., 1980, 8-9.
- R. Ger, On functional inequalities stemming from stability questions, Internat. Ser. Numer. Math. 103 (1992), 227-240.
- R. Ger, The singular case in the stability behaviour of linear mappings, submitted to the Proceedings of the Austrian-Polish Seminar on Functional Equations and Iterations, Graz, October 1991.
- L. Nachbin, A theorem of the Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc. 68 (1950), 28-46.
- D. Yost, Talk at the 17th Winter School on Abstract Analysis (Section of Analysis), Šrni, January 1989.
- D. Yost, Talk at the 18th Winter School on Abstract Analysis (Section of Analysis), Šrni, January 1990.
Pages:
243-252
Main language of publication
English
Received
1991-07-29
Accepted
1992-02-10
Published
1992
Exact and natural sciences