Abstract
A functional equation involving pairs of means is considered. It is shown that there are only constant solutions if continuous differentiability is assumed, and there may be non-constant everywhere differentiable solutions. Various other situations are considered, where less smoothness is assumed on the unknown function.
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Communicated by L. Kérchy
Supported by the Hungarian Scientific Research Fund (OTKA) Grant NK 111651.
Supported by the European Research Council Advanced Grant No. 267055.
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Daróczy, Z., Totik, V. Remarks on a functional equation. ActaSci.Math. 81, 527–534 (2015). https://doi.org/10.14232/actasm-015-805-1
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DOI: https://doi.org/10.14232/actasm-015-805-1