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On a class of functional equations which includes the Pexider's one

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Abstract

We find the solutions \(f,g,h \colon S \to H\) of the following extension of Pexider's functional equation

$$\underset{\lambda\in K}{\sum}f(x+\lambda y)=g(x)+h(y),\quad x,y\in S,$$

where (S,+) is an abelian semigroup, K is a finite subgroup of the automorphism group of S and (H,+) is an abelian group.

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Acknowledgement

We wish to express our thanks to the referee for useful comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Chouaïb Doukkali University, B.P. 20, El Jadida, Morocco

    B. Fadli

  2. Department of Mathematics, E.N.S.A.M, Moulay Ismail University, B.P. 15290, Al Mansour, Meknes, Morocco

    D. Zeglami

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  1. B. Fadli
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  2. D. Zeglami
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Correspondence to B. Fadli.

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Fadli, B., Zeglami, D. On a class of functional equations which includes the Pexider's one. Acta Math. Hungar. 165, 63–77 (2021). https://doi.org/10.1007/s10474-021-01175-1

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  • DOI: https://doi.org/10.1007/s10474-021-01175-1

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