On the functional inequality \(f(x+y)+f(xy){\geq}f(x)+f(y)+f(x)f(y)\) (Q1801348)
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scientific article; zbMATH DE number 202391
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the functional inequality \(f(x+y)+f(xy){\geq}f(x)+f(y)+f(x)f(y)\) |
scientific article; zbMATH DE number 202391 |
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On the functional inequality \(f(x+y)+f(xy){\geq}f(x)+f(y)+f(x)f(y)\) (English)
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26 May 1994
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The author proves that if \(f:\mathbb{R} \to \mathbb{R}\) is a continuous and differentiable at zero solution of the functional inequality \(f(x+y)+f(xy) \geq f(x)+f(y) +f(x)f(y)\), \(x,y \in \mathbb{R}\), then \(f(x)=0\) or \(f(x)=x+((a-1)/a) (e^{ax}-1)\) for an \(a \geq 1\).
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differentiable solution
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functional inequality
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