Aequationes mathematicae

, Volume 93, Issue 6, pp 1275–1291 | Cite as

A note on the Levi-Civita functional equation

  • Keltouma Belfakih
  • Elhoucien ElqorachiEmail author


In this paper we find the solutions of the functional equation
$$\begin{aligned} f(xy)=g(x)h(y)+\sum _{j=1}^{n}g_j(x)h_j(y),\;x,y \in M, \end{aligned}$$
where M is a monoid, \(n\ge 2\), and \(g_j\) (for \(j=1,\ldots ,n\)) are linear combinations of at least 2 distinct nonzero multiplicative functions.


Sine addition formula Levi-Civita functional equation Monoid Functional equation Multiplicative function 

Mathematics Subject Classification

39B52 39B32 



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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesUniversity Ibn ZohrAgadirMorocco

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