On a modified Hyers-Ulam stability of homogeneous equation (Q1392696)
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scientific article; zbMATH DE number 1180638
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a modified Hyers-Ulam stability of homogeneous equation |
scientific article; zbMATH DE number 1180638 |
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On a modified Hyers-Ulam stability of homogeneous equation (English)
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4 March 1999
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The following Hyers-Ulam stability results is given: If \(f\) satisfies the inequality \[ \bigl\| f(yx) -y^kf(x) \bigr\| \leq\varphi (x,y), \] then (under suitable assumptions) there exists a unique function \(T\) satisfying the homogeneous equation \(T(xy)= y^kT(x)\) such that \(\| T(x)- f(x)\| \leq\Phi(x)\).
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functional equations
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Hyers-Ulam stability
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homogeneous equation
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0.9272843
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0.9253847
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0.91764134
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0.9153315
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