Abstract
In this paper we prove that if a generalized polynomial function f satisfies the condition f(x) f(y) = 0 for all solutions of the equation x 2 + y 2 = 1, then f is identically equal to 0.
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Dedicated to Prof. János Aczél on the occassion of his 90th birthday
Research of Z. Boros has been supported by the Hungarian Scientific Research Fund (OTKA) Grant NK 81402 (contributing to the technical and logistic background) and by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP 4.2.4.A/2-11/1-2012-0001 ’National Excellence Program’ (providing personal grant). Research of W. Fechner was supported by the Polish Ministry of Science and Higher Education in the years 2013–2014, under project No IP2012 011072.
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Boros, Z., Fechner, W. An alternative equation for polynomial functions. Aequat. Math. 89, 17–22 (2015). https://doi.org/10.1007/s00010-014-0258-6
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DOI: https://doi.org/10.1007/s00010-014-0258-6