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Wilson’s functional equation on monoids with involutive automorphisms

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Abstract

In the present paper, we determine the complex-valued solutions (f, g) of the functional equation

$$f(x\sigma(y))+f(\tau(y)x)=2f(x)g(y),$$

in the setting of groups and monoids that need not be abelian, where \({\sigma,\tau}\) are involutive automorphisms. We prove that their solutions can be expressed in terms of multiplicative and additive functions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Ibn Tofail University, BP: 14000, Kenitra, Morocco

    Kh. Sabour, B. Fadli & S. Kabbaj

Authors
  1. Kh. Sabour
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  2. B. Fadli
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  3. S. Kabbaj
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Correspondence to B. Fadli.

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Sabour, K., Fadli, B. & Kabbaj, S. Wilson’s functional equation on monoids with involutive automorphisms. Aequat. Math. 90, 1001–1011 (2016). https://doi.org/10.1007/s00010-016-0435-x

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  • DOI: https://doi.org/10.1007/s00010-016-0435-x

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