Published: 2024-12-25

Functional equations with an anti-endomorphism for functions with multidimensional codomains

Ayoub Ouhabi Logo ORCID , Driss Zeglami , Mohamed Ayoubi

Abstract

Let S be a semigroup, ℍ be the skew field of quaternions, and ψ: SS be an anti-endomorphism. We determine the general solution of the functional equation
g(xy) - g(xψ(y)) = 2g(x)g(y),    x,yS,
where g: S→ℂ is the unknown function. And when S = M is a monoid, we solve the functional equation
g(xy) + g(xψ(y)) = 2g(x)g(y),   x,yM,
where g: M→ℍ is the unknown function.

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Ouhabi, A., Zeglami, D., & Ayoubi, M. (2024). Functional equations with an anti-endomorphism for functions with multidimensional codomains. Annales Mathematicae Silesianae. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/18252

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2024
Published: 2024-01-18


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

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