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

top
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

top

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

top
  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. 

NotesEmbed ?

top

You must be logged in to post comments.