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Zbl 1146.39045
Lee, Jung Rye; An, Jong Su; Park, Choonkil
On the stability of quadratic functional equations. (English)
[J] Abstr. Appl. Anal. 2008, Article ID 628178, 8 p. (2008). ISSN 1085-3375; ISSN 1687-0409/e

Summary: Let $X,Y$ be vector spaces and $k$ a fixed positive integer. It is shown that a mapping $f(kx+y)+f(kx-y)=2k^{2}f(x)+2f(y)$ for all $x,y\in X$ if and only if the mapping $f:X\rightarrow Y$ satisfies $f(x+y)+f(x-y)=2f(x)+2f(y)$ for all $x,y\in X$. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven.

MSC 2000:: *39B82 Stability, separation, extension, and related topics
39B52 Functional equations for functions with more general domains

Keywords: Hyers-Ulam-Rassias stability; Banach spaces

Cited in: Zbl 1205.39023 Zbl 1189.39031 Zbl 1168.39011

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