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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.

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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