A characterization of continuous associative operations whose graphs are ruled surfaces (Q579542)
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scientific article; zbMATH DE number 4015333
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of continuous associative operations whose graphs are ruled surfaces |
scientific article; zbMATH DE number 4015333 |
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A characterization of continuous associative operations whose graphs are ruled surfaces (English)
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1987
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The authors characterize a class of continuous associative binary operations. The characterization is reduced to solving the following functional equation for f: [0,\(\infty)\to [0,\infty):\) \(f^{- 1}(f(x)/f(x+y))+f^{-1}(f(y)/f(x+y))=1,\) \(x+y>0\), whose strictly increasing solutions are determined and are of the form \(f(x)=x^ c\), \(c>0\).
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surface in 3-space
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continuous associative binary operations
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