## Abstract and Applied Analysis

### On the Stability of Quadratic Functional Equations

#### Abstract

Let $X,Y$ be vector spaces and $k$ a fixed positive integer. It is shown that a mapping $f(kx+y)+f(kx-y)=2{k}^{2}f(x)+2f(y)$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 628178, 8 pages.

Dates
First available in Project Euclid: 9 September 2008

https://projecteuclid.org/euclid.aaa/1220969154

Digital Object Identifier
doi:10.1155/2008/628178

Mathematical Reviews number (MathSciNet)
MR2393119

Zentralblatt MATH identifier
1146.39045

#### Citation

Lee, Jung Rye; An, Jong Su; Park, Choonkil. On the Stability of Quadratic Functional Equations. Abstr. Appl. Anal. 2008 (2008), Article ID 628178, 8 pages. doi:10.1155/2008/628178. https://projecteuclid.org/euclid.aaa/1220969154

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