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2008 On the Stability of Quadratic Functional Equations
Jung Rye Lee, Jong Su An, Choonkil Park
Abstr. Appl. Anal. 2008: 1-8 (2008). DOI: 10.1155/2008/628178

Abstract

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

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Jung Rye Lee. Jong Su An. Choonkil Park. "On the Stability of Quadratic Functional Equations." Abstr. Appl. Anal. 2008 1 - 8, 2008. https://doi.org/10.1155/2008/628178

Information

Published: 2008
First available in Project Euclid: 9 September 2008

zbMATH: 1146.39045
MathSciNet: MR2393119
Digital Object Identifier: 10.1155/2008/628178

Rights: Copyright © 2008 Hindawi

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