A theorem of the Hahn-Banach type and its applications

Zbigniew Gajda; Andrzej Smajdor; Wilhelmina Smajdor

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 3, page 243-252
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Zbigniew Gajda, Andrzej Smajdor, and Wilhelmina Smajdor. "A theorem of the Hahn-Banach type and its applications." Annales Polonici Mathematici 57.3 (1992): 243-252. <http://eudml.org/doc/275917>.

@article{ZbigniewGajda1992,
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.},
author = {Zbigniew Gajda, Andrzej Smajdor, Wilhelmina Smajdor},
journal = {Annales Polonici Mathematici},
keywords = {Hahn-Banach theorem; additive selection; subadditive set-valued function; binary intersection property; stability of functional equations},
language = {eng},
number = {3},
pages = {243-252},
title = {A theorem of the Hahn-Banach type and its applications},
url = {http://eudml.org/doc/275917},
volume = {57},
year = {1992},
}

TY - JOUR
AU - Zbigniew Gajda
AU - Andrzej Smajdor
AU - Wilhelmina Smajdor
TI - A theorem of the Hahn-Banach type and its applications
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 3
SP - 243
EP - 252
AB - 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.
LA - eng
KW - Hahn-Banach theorem; additive selection; subadditive set-valued function; binary intersection property; stability of functional equations
UR - http://eudml.org/doc/275917
ER -

References

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  1. [1] J. Aczél, Lectures on Functional Equations and their Applications, Academic Press, New York 1966. Zbl0139.09301
  2. [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. [3] R. Ger, On functional inequalities stemming from stability questions, Internat. Ser. Numer. Math. 103 (1992), 227-240. Zbl0770.39007
  4. [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. [5] L. Nachbin, A theorem of the Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc. 68 (1950), 28-46. Zbl0035.35402
  6. [6] D. Yost, Talk at the 17th Winter School on Abstract Analysis (Section of Analysis), Šrni, January 1989. 
  7. [7] D. Yost, Talk at the 18th Winter School on Abstract Analysis (Section of Analysis), Šrni, January 1990. 

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