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Nonlinear stability of a quadratic functional equation with complex involution. (English) Zbl 1249.39031
Motivated by the paper [C. Park and 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.

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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