# On Baire measurable solutions of some functional equations

Open Mathematics (2009)

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

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topKarol 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

top- [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] Járai A., Regularity properties of functional equations in several variables, Springer, 2005 Zbl1081.39022
- [3] Kochanek T., Lewicki M., On measurable solutions of a general functional equation on topological groups, preprint Zbl1274.39046
- [4] Kuratowski K., Topology, Academic Press & PWN-Polish Scientific Publishers, 1966
- [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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