Abstract
We analyse the composite functional equation \(f(x+2f(y))=f(x)+y+f(y)\) on certain groups. In particular we give a description of solutions on abelian 3-groups and finitely generated free abelian groups. This is motivated by a work of Pál Burai, Attila Házy and Tibor Juhász, who described the solutions of the equation on uniquely 3-divisible abelian groups.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Boros, Z., Daróczy, Z.: A composite functional equation with additive solutions. Publ. Math. Debrecen 69(1–2), 245–253 (2006)
Burai, P., Házy, A., Juhász, T.: A composite functional equation from algebraic aspect. Aequationes Math. 86, 57–64 (2013)
Chao, W.W.: Problems and solutions: problems: 10854. Am. Math. Mon. 108(2), 171 (2001)
Chao, W.W., Henderson, D.: Continuous additive functions: 10854. Am. Math. Mon. 111(8), 725–726 (2004)
Fuchs, L.: Abelian Groups. Publishing House of the Hungarian Academy of Sciences, Budapest (1958)
Griffin, H.: Elementary Theory of Numbers. McGraw-Hill, New York (1954)
Kurzweil, H., Stellmacher, B.: The Theory of Finite Groups. Springer, New York (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Toborg, I. A composite functional equation on groups. Aequat. Math. 91, 289–299 (2017). https://doi.org/10.1007/s00010-016-0454-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00010-016-0454-7