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http://dx.doi.org/10.4134/CKMS.c190326

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)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.3, 2020 , pp. 711-722 More about this Journal
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.
Keywords
Semigroup; involutive automorphism; multiplicative function; d'Alembert's equation; Wilson's equation;
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