In this paper we discuss the composite functional equation
on an Abelian group. This equation originates from Problem 10854 of the American Mathematical Monthly. We give an algebraic description of the solutions on uniquely 3-divisible Abelian groups, and then we construct all solutions f of this equation on finite Abelian groups without elements of order 3 and on divisible Abelian groups without elements of order 3 including the additive group of real numbers.
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This research has been supported by the Hungarian Scientific Research Fund (OTKA) Grant NK-81402 and OTKA “Mobility” call Human-MB08A-84581. The second-named author’s research was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.
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Burai, P., Házy, A. & Juhász, T. A composite functional equation from algebraic aspect. Aequat. Math. 86, 57–64 (2013). https://doi.org/10.1007/s00010-013-0211-0
Mathematics Subject Classification (2010)
- Composite functional equation
- iterative functional equation
- additive mapping
- Hamel basis
- Abelian group