On Baire measurable solutions of some functional equations

Karol Baron

Open Mathematics (2009)

  • Volume: 7, Issue: 4, page 804-808
  • ISSN: 2391-5455

Abstract

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We establish conditions under which Baire measurable solutions f of Γ ( x , y , | f ( x ) - f ( y ) | ) = Φ ( x , y , f ( x + φ 1 ( y ) ) , . . . , f ( x + φ N ( y ) ) ) defined on a metrizable topological group are continuous at zero.

How to cite

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Karol Baron. "On Baire measurable solutions of some functional equations." Open Mathematics 7.4 (2009): 804-808. <http://eudml.org/doc/269725>.

@article{KarolBaron2009,
abstract = {We establish conditions under which Baire measurable solutions f of \[ \Gamma (x,y,|f(x) - f(y)|) = \Phi (x,y,f(x + \phi \_1 (y)),...,f(x + \phi \_N (y))) \] defined on a metrizable topological group are continuous at zero.},
author = {Karol Baron},
journal = {Open Mathematics},
keywords = {Functional equations in several variables; Baire measurable solutions; Metrizable topological groups; functional equations in several variables, Baire measurable solutions; metrizable topological groups},
language = {eng},
number = {4},
pages = {804-808},
title = {On Baire measurable solutions of some functional equations},
url = {http://eudml.org/doc/269725},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Karol Baron
TI - On Baire measurable solutions of some functional equations
JO - Open Mathematics
PY - 2009
VL - 7
IS - 4
SP - 804
EP - 808
AB - We establish conditions under which Baire measurable solutions f of \[ \Gamma (x,y,|f(x) - f(y)|) = \Phi (x,y,f(x + \phi _1 (y)),...,f(x + \phi _N (y))) \] defined on a metrizable topological group are continuous at zero.
LA - eng
KW - Functional equations in several variables; Baire measurable solutions; Metrizable topological groups; functional equations in several variables, Baire measurable solutions; metrizable topological groups
UR - http://eudml.org/doc/269725
ER -

References

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  1. [1] Grosse-Erdmann K.-G., Regularity properties of functional equations, Aequations Math., 1989, 37, 233–251 http://dx.doi.org/10.1007/BF01836446[Crossref] Zbl0676.39007
  2. [2] Járai A., Regularity properties of functional equations in several variables, Springer, 2005 Zbl1081.39022
  3. [3] Kochanek T., Lewicki M., On measurable solutions of a general functional equation on topological groups, preprint Zbl1274.39046
  4. [4] Kuratowski K., Topology, Academic Press & PWN-Polish Scientific Publishers, 1966 
  5. [5] Volkmann P., On the functional equation min{f(x + y); f(x − y)} = |f(x − f(y)|, talk at the Seminar on Functional Equations and Inequalities in Several Variables in the Silesian University Mathematics Department on January 19, 2009 

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