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On stability of a functional equation connected with the Reynolds operator. (English) Zbl 1133.39031

Summary: Let \((X,\circ)\) be an Abelian semigroup, \(g:X\to X\), and let \(\mathbb K\) be either \(\mathbb R\) or \(\mathbb C\). We prove superstability of the functional equation \(f(x\circ g(y))=f(x)f(y)\) in the class of functions \(f:X\to \mathbb K\). We also show some stability results of the equation in the class of functions \(f:X\to \mathbb K^n\).

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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References:

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