Baron, Karol On Baire measurable solutions of some functional equations. (English) Zbl 1190.39013 Cent. Eur. J. Math. 7, No. 4, 804-808 (2009). Author’s summary: 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. Reviewer: Claudi Alsina (Barcelona) Cited in 2 Documents MSC: 39B52 Functional equations for functions with more general domains and/or ranges Keywords:functional equations in several variables, Baire measurable solutions; metrizable topological groups PDFBibTeX XMLCite \textit{K. Baron}, Cent. Eur. J. Math. 7, No. 4, 804--808 (2009; Zbl 1190.39013) Full Text: DOI References: [1] Grosse-Erdmann K.-G., Regularity properties of functional equations, Aequations Math., 1989, 37, 233-251 http://dx.doi.org/10.1007/BF01836446; · Zbl 0676.39007 [2] Járai A., Regularity properties of functional equations in several variables, Springer, 2005; · Zbl 1081.39022 [3] Kochanek T., Lewicki M., On measurable solutions of a general functional equation on topological groups, preprint; · Zbl 1274.39046 [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; This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.