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Some trigonometric functional equations on monoids generated by their squares

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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 f, h, k on monoids generated by their squares. Here \(\sigma \) and \(\tau \) are involutive automorphisms of the monoid.

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  1. Department of Mathematics, University of Louisville, Louisville, Kentucky, 40292, USA

    Bruce Ebanks

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  1. Bruce Ebanks
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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. 95, 383–391 (2021). https://doi.org/10.1007/s00010-020-00730-5

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  • DOI: https://doi.org/10.1007/s00010-020-00730-5

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