Some trigonometric functional equations on monoids generated by their squares

Our main result is the solution of the functional equation f ( x σ ( y ) ) + h ( τ ( y ) x ) = 2 f ( x ) k ( y ) for complex-valued functions f ,  h ,  k on monoids generated by their squares. Here σ and τ are involutive automorphisms of the monoid.

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Bibliographic Details
Published in:Aequationes mathematicae 2021-04, Vol.95 (2), p.383-391
Main Author: Ebanks, Bruce
Format: Article
Language:English
Subjects:
Analysis
Automorphisms
Combinatorics
Functional equations
Mathematics
Mathematics and Statistics
Monoids
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Summary:Our main result is the solution of the functional equation f ( x σ ( y ) ) + h ( τ ( y ) x ) = 2 f ( x ) k ( y ) for complex-valued functions f ,  h ,  k on monoids generated by their squares. Here σ and τ are involutive automorphisms of the monoid.
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-020-00730-5