Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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VARIANTS OF WILSON'S FUNCTIONAL EQUATION ON SEMIGROUPS

  • Ajebbar, Omar (Department of Mathematics Faculty of Sciences Ibn Zohr University) ;
  • Elqorachi, Elhoucien (Department of Mathematics Faculty of Sciences Ibn Zohr University)
  • Received : 2019.09.16
  • Accepted : 2019.12.26
  • Published : 2020.07.31
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Abstract

Given a semigroup S generated by its squares equipped with an involutive automorphism 𝝈 and a multiplicative function 𝜇 : S → ℂ such that 𝜇(x𝜎(x)) = 1 for all x ∈ S, we determine the complex-valued solutions of the following functional equations f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(x)g(y), x, y ∈ S and f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(y)g(x), x, y ∈ S.

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References

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