Skip to main content

On the functional equation \({\varvec{f}}({\varvec{x}})+{\varvec{f}}({\varvec{y}})=\mathbf{max} \{{\varvec{f}}({\varvec{xy}}),{\varvec{f}}({\varvec{xy}}^{-{\varvec{1}}})\}\) on groups

Archiv der Mathematik volume 109, pages 215–221 (2017)Cite this article

Abstract

We analyse the functional equation

$$\begin{aligned} f(x)+f(y)=\max \{f(xy),f(xy^{-1})\} \end{aligned}$$

for a function \(f:G\rightarrow \mathbb R\) where G is a group. Without further assumption it characterises the absolute value of additive functions. In addition \(\{z\in G\mid f(z)=0\}\) is a normal subgroup of G with abelian factor group.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. R. Badora, B. Przebieracz, and  P. Volkmann, On Tabor groupoids and stability of some functional equations, Aequationes Math. 87 (2014), 165–171.

    MathSciNet  Article  MATH  Google Scholar 

  2. W. Jarczyk and  P. Volkmann, On functional equations in connection with the absolute value of additive functions, Series Math. Catovic. Debrecen. 32 (2010), 11 pp.

  3. A. Simon (Chaljub-Simon) and  P. Volkmann, Caractérisation du module d’une fonction additive à l’aide d’une équation fonctionnelle, Aequationes Math. 47 (1994), 60–68.

    Google Scholar 

  4. P. Volkmann, Charakterisierung des Betrages reellwertiger additiver Funktionen auf Gruppen, KITopen (2017), 4pp.

Download references

Author information

Authors and Affiliations

  1. Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099, Halle (Saale), Germany

    Imke Toborg

Authors
  1. Imke Toborg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Imke Toborg.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Toborg, I. On the functional equation \({\varvec{f}}({\varvec{x}})+{\varvec{f}}({\varvec{y}})=\mathbf{max} \{{\varvec{f}}({\varvec{xy}}),{\varvec{f}}({\varvec{xy}}^{-{\varvec{1}}})\}\) on groups. Arch. Math. 109, 215–221 (2017). https://doi.org/10.1007/s00013-017-1061-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-017-1061-0

Mathematics Subject Classification

  • 39B52
  • 20F99

Keywords

  • Absolute value of additive functions
  • Functional equations on groups
  • Maximum equation