Nonlinear stability of a quadratic functional equation with complex involution. (English) Zbl 1249.39031

Saadati, Reza; Sadeghi, Ghadir

Arch. Math., Brno 47, No. 2, 111-117 (2011).

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.

Reviewer: Ondřej Došlý (Brno)

MSC:

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

Keywords:

quadratic functional equation; generalized Hyers-Ulam stability; fixed point method

Citations:

Zbl 1144.39028