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A composite functional equation on groups

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.

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Correspondence to Imke Toborg.

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Toborg, I. A composite functional equation on groups. Aequat. Math. 91, 289–299 (2017). https://doi.org/10.1007/s00010-016-0454-7

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  • DOI: https://doi.org/10.1007/s00010-016-0454-7

Mathematics Subject Classification

  • 20K10
  • 20K15
  • 20D45
  • 39B12
  • 39B52

Keywords

  • Composite functional equation
  • Torsion group
  • 3-group
  • Finitely generated abelian group