A generalization of the cosine addition law on semigroups

Our main result is that we describe the solutions g , f : S → C of the functional equation g ( x σ ( y ) ) = g ( x ) g ( y ) - f ( x ) f ( y ) + α f ( x σ ( y ) ) , x , y ∈ S , where S is a semigroup, α ∈ C is a fixed constant and σ : S → S an involutive automorphism.

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Bibliographic Details
Published in:Aequationes mathematicae 2023-08, Vol.97 (4), p.787-804
Main Authors: Aserrar, Youssef, Elqorachi, Elhoucien
Format: Article
Language:English
Subjects:
Analysis
Automorphisms
Combinatorics
Functional equations
Mathematics
Mathematics and Statistics
Semigroups
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Summary:Our main result is that we describe the solutions g , f : S → C of the functional equation g ( x σ ( y ) ) = g ( x ) g ( y ) - f ( x ) f ( y ) + α f ( x σ ( y ) ) , x , y ∈ S , where S is a semigroup, α ∈ C is a fixed constant and σ : S → S an involutive automorphism.
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-023-00946-1