On the Stability of Quadratic Functional Equations
Jung Rye Lee, Jong Su An, and Choonkil Park
Source: Abstr. Appl. Anal. Volume 2008 (2008), 8 pages.
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aaa/1220969154
Digital Object Identifier: doi:10.1155/2008/628178
Mathematical Reviews number (MathSciNet):
MR2393119
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Abstract and Applied Analysis
