Note on a functional equation related to the power means (Q2714287)
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scientific article; zbMATH DE number 1604180
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Note on a functional equation related to the power means |
scientific article; zbMATH DE number 1604180 |
Statements
13 June 2001
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weighted quasi-arithmetic mean
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additive function
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exponential function
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0.9708325
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0.9115746
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0.90438235
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0.8966089
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0.8931054
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0.8837075
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0.87472725
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Note on a functional equation related to the power means (English)
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Solutions of the functional equation \( x + g(y + f(x)) = y + g(x + f(y)) \) are determined under the assumption that (at least) one of the unknown functions is additive or has the form of a weighted quasi-arithmetic mean with an exponential generator. Continuity assumptions are required when \(f\) is supposed to belong to a given class.
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