A theorem of the Hahn-Banach type and its applications

• Autorzy: Zbigniew Gajda , Andrzej Smajdor , Wilhelmina Smajdor
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Hahn-Banach theorem; additive selection; subadditive set-valued function; binary intersection property; stability of functional equations

Kategorie tematyczne

• 46A22: Theorems of Hahn-Banach type; extension and lifting of functionals and operators
• 39B99: None of the above, but in this section
• 26E25: Set-valued functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1992
• Tom: 57
• Numer: 3
• Strony: 243-252

Daty

wydano

1992

otrzymano

1991-07-29

poprawiono

1992-02-10

Twórcy

autor

Zbigniew Gajda

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

autor

Andrzej Smajdor

• Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

autor

Wilhelmina Smajdor

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] J. Aczél, Lectures on Functional Equations and their Applications, Academic Press, New York 1966.
• [2] 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.
• [3] R. Ger, On functional inequalities stemming from stability questions, Internat. Ser. Numer. Math. 103 (1992), 227-240.
• [4] 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.
• [5] L. Nachbin, A theorem of the Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc. 68 (1950), 28-46.
• [6] D. Yost, Talk at the 17th Winter School on Abstract Analysis (Section of Analysis), Šrni, January 1989.
• [7] D. Yost, Talk at the 18th Winter School on Abstract Analysis (Section of Analysis), Šrni, January 1990.