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Nonlinear Functional Equations and Eigenvalue Problems in Nonseperable Banach Spaces

Peter Hess (1971)

Commentarii mathematici Helvetici

Nonlinear functional equations and their Baire category properties.

Witold Jarczyk (1986)

Aequationes mathematicae

Nonlinear stability of a quadratic functional equation with complex involution

Reza Saadati, Ghadir Sadeghi (2011)

Archivum Mathematicum

Let $X, Y$ be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping $f : X \to Y$ satisfies $\begin{matrix} f (x + i y) + f (x - i y) = 2 f (x) - 2 f (y) \end{matrix}$ for all $x$ , $y \in X$ , then the mapping $f : X \to Y$ satisfies $f (x + y) + f (x - y) = 2 f (x) + 2 f (y)$ for all $x$ , $y \in X$ . Furthermore, they proved the generalized Hyers-Ulam stability of the functional equation () in complex Banach spaces. In this paper, we will adopt the idea of Park and Th. M. Rassias to prove the stability of a quadratic functional equation with complex involution via fixed point method.