Stability of the generalized alternative Cauchy equation (Q1969676)
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scientific article; zbMATH DE number 1416705
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability of the generalized alternative Cauchy equation |
scientific article; zbMATH DE number 1416705 |
Statements
Stability of the generalized alternative Cauchy equation (English)
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19 March 2000
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Let \(G\) be a commutative semigroup and let \(L\) be a complete Archimedean Riesz space. Suppose that \(F: G\to L\) satisfies for some \(e\in L_+\) the inequality \[ \biggl||F(x+ y)|-|F(x)+ F(y)|\biggr|\leq e\quad\text{for }x,y\in G. \] Then there exists a unique additive mapping \(A: G\to L\) such that \[ |F(x)- A(x)|\leq e\quad\text{for }x\in G. \]
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stability
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alternative Cauchy equation
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functional inequality
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commutative semigroup
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Archimedean Riesz space
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