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Aequationes mathematicae

, Volume 86, Issue 1–2, pp 57–64 | Cite as

A composite functional equation from algebraic aspect

Article

Abstract

In this paper we discuss the composite functional equation
$$f(x+2f(y)) = f(x)+y+f(y)$$
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.

Mathematics Subject Classification (2010)

39B12 39B52 

Keywords

Composite functional equation iterative functional equation additive mapping automorphism Hamel basis Abelian group 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Probability TheoryUniversity of DebrecenDebrecenHungary
  2. 2.TU Berlin Institut für MathematikBerlinGermany
  3. 3.Department of Applied MathematicsUniversity of MiskolcMiskolc-EgyetemvárosHungary
  4. 4.Institute of Mathematics and InformaticsEszterházy Károly CollegeEgerHungary

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