Abstract and Applied Analysis

A Functional Equation Originating from Elliptic Curves

Won-Gil Park and Jae-Hyeong Bae

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Abstract

We obtain the general solution and the stability of the functional equation f ( x + y + z , u + v + w ) + f ( x + y z , u + v + w ) + 2 f ( x , u w ) + 2 f ( y , v w ) = f ( x + y , u + w ) + f ( x + y , v + w ) + f ( x + z , u + w ) + f ( x z , u + v w ) + f ( y + z , v + w ) + f ( y z , u + v w ) . The function f ( x , y ) = x 3 + a x + b y 2 having level curves as elliptic curves is a solution of the above functional equation.

Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 135237, 10 pages.

Dates
First available in Project Euclid: 9 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1220969161

Digital Object Identifier
doi:10.1155/2008/135237

Mathematical Reviews number (MathSciNet)
MR2407274

Zentralblatt MATH identifier
1146.39037

Citation

Park, Won-Gil; Bae, Jae-Hyeong. A Functional Equation Originating from Elliptic Curves. Abstr. Appl. Anal. 2008 (2008), Article ID 135237, 10 pages. doi:10.1155/2008/135237. https://projecteuclid.org/euclid.aaa/1220969161


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