Aequationes mathematicae

, Volume 89, Issue 1, pp 49–56 | Cite as

Stability of generalized Cauchy equations

  • Roman Badora
  • Barbara Przebieracz
  • Peter Volkmann
Open Access


We investigate the stability of the functional equation
$$f(xy) = g(x)h(y) + k(y)$$
on amenable semigroups. This equation is a common generalization of two Pexider equations stemming from Cauchy’s additive and multiplicative functional equations, and it is a simple case of the Levi-Civita equation.


Cauchy equations stability in the sense of Hyers–Ulam Pexider equations Levi-Civita functional equation 

Mathematics Subject Classification

Primary 39B82 Secondary 39B22 


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Copyright information

© The Author(s) 2014

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  • Roman Badora
    • 1
  • Barbara Przebieracz
    • 1
  • Peter Volkmann
    • 2
  1. 1.Instytut MatematykiUniwersytet Śla̧skiKatowicePoland
  2. 2.Institut für AnalysisKITKarlsruheGermany

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