Some trigonometric functional equations on monoids generated by their squares

Abstract

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

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Correspondence to Bruce Ebanks.

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Ebanks, B. Some trigonometric functional equations on monoids generated by their squares. Aequat. Math. (2020). https://doi.org/10.1007/s00010-020-00730-5

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Mathematics Subject Classification

  • 39B32
  • 39B52

Keywords

  • Involution
  • Automorphism
  • Trigonometric functional equation
  • Monoid
  • d’Alembert