Nonlinear stability of a quadratic functional equation with complex involution. (Q2897383)
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scientific article; zbMATH DE number 6054251
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear stability of a quadratic functional equation with complex involution. |
scientific article; zbMATH DE number 6054251 |
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10 July 2012
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quadratic functional equation
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generalized Hyers-Ulam stability
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fixed point method
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Nonlinear stability of a quadratic functional equation with complex involution. (English)
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Motivated by the paper [\textit{C. Park} and \textit{T. M. Rassias}, Math. Inequal. 1, No. 4, 515--528 (2007; Zbl 1144.39028)] the authors investigate Hayers-Ulam stability of the functional equation in a complex vector space \(f(x+\rho (y))+f(x-\rho (y))=2f(x)+2f(y)\), where the mapping \(\rho \) satisfies \(\rho (\rho (x))=-x\). The main result of the paper, which is rather complicated to be presented in a brief way, concerns stability of the above equation and is proved via the fixed point method.
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