On Baire measurable solutions of some functional equations

• Autorzy: Karol Baron
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Functional equations in several variables; Baire measurable solutions; Metrizable topological groups

Kategorie tematyczne

• 39B22: Equations for real functions
• 39B52: Equations for functions with more general domains and/or ranges

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 4
• Strony: 804-808

Daty

wydano

2009-12-01

online

2009-10-31

Twórcy

autor

Karol Baron

• Instytut Matematyki, Uniwersytet Šla̧ski, Katowice, Poland

Bibliografia

• [1] Grosse-Erdmann K.-G., Regularity properties of functional equations, Aequations Math., 1989, 37, 233–251 http://dx.doi.org/10.1007/BF01836446[Crossref]
• [2] Járai A., Regularity properties of functional equations in several variables, Springer, 2005
• [3] Kochanek T., Lewicki M., On measurable solutions of a general functional equation on topological groups, preprint
• [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

Identyfikatory

DOI

10.2478/s11533-009-0042-3