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A generalization of d’Alembert’s other functional equation on semigroups

  • Omar AjebbarEmail author
  • Elhoucien Elqorachi
Article
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Abstract

Given a semigroup S generated by its squares and equipped with an involutive automorphism \(\sigma \) and a multiplicative function \(\mu :S\rightarrow \mathbb {C}\) such that \(\mu (x\sigma (x))=1\) for all \(x\in S\), we determine the complex-valued solutions of the following functional equation
$$\begin{aligned} f(xy)-\mu (y)f(\sigma (y)x)=g(x)h(y),\quad x,y\in S. \end{aligned}$$

Keywords

Semigroup Involutive automorphism Multiplicative function d’Alembert equation 

Mathematics Subject Classification

Primary 39B52 Secondary 39B32 

Notes

References

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesIbn Zohr UniversityAgadirMorocco

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