A Functional Equation Originating from Elliptic Curves

Won-Gil Park and Jae-Hyeong Bae

Abstract and Applied Analysis, 2008, vol. 2008, issue 1

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) + 2f(x, u − w) + 2f(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) = x3 + ax + b − y2 having level curves as elliptic curves is a solution of the above functional equation.

Date: 2008
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https://doi.org/10.1155/2008/135237

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:135237

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