Abstract and Applied Analysis

On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations

M. Eshaghi Gordji and H. Khodaei

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Abstract

We achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations f ( a x + b y ) + f ( a x b y ) = ( b ( a + b ) / 2 ) f ( x + y ) + ( b ( a + b ) / 2 ) f ( x y ) + ( 2 a 2 a b b 2 ) f ( x ) + ( b 2 a b ) f ( y ) where a, b are nonzero fixed integers with b ± a , 3 a , and f ( a x + b y ) + f ( a x b y ) = 2 a 2 f ( x ) + 2 b 2 f ( y ) for fixed integers a, b with a , b 0 and a ± b 0 .

Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 923476, 11 pages.

Dates
First available in Project Euclid: 16 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1268745570

Digital Object Identifier
doi:10.1155/2009/923476

Mathematical Reviews number (MathSciNet)
MR2516012

Zentralblatt MATH identifier
1167.39014

Citation

Gordji, M. Eshaghi; Khodaei, H. On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations. Abstr. Appl. Anal. 2009 (2009), Article ID 923476, 11 pages. doi:10.1155/2009/923476. https://projecteuclid.org/euclid.aaa/1268745570


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