Quaternion-valued d’Alembert functions on semigroups

Let S be a semigroup with an involution τ (meaning that it is an involutive anti-automorphism of S )and let H be the skew field of quaternions. Our main goal is to solve d’Alembert’s quaternion functional equation L ( x y ) + L ( x τ ( y ) ) = 2 L ( x ) L ( y ) , x , y ∈ S , where L : S → H is the u...

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Bibliographic Details
Published in:Boletín de la Sociedad Matemática Mexicana 2024-07, Vol.30 (2), Article 66
Main Authors: Ouhabi, Ayoub, Zeglami, Driss, Ayoubi, Mohamed
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Original Article
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Summary:Let S be a semigroup with an involution τ (meaning that it is an involutive anti-automorphism of S )and let H be the skew field of quaternions. Our main goal is to solve d’Alembert’s quaternion functional equation L ( x y ) + L ( x τ ( y ) ) = 2 L ( x ) L ( y ) , x , y ∈ S , where L : S → H is the unknown function.
ISSN:1405-213X
2296-4495
DOI:10.1007/s40590-024-00636-1