A Functional Equation Originating from Elliptic Curves

Won-Gil Park and Jae-Hyeong Bae

Abstract and Applied Analysis, 2008, vol. 2008, 1-10

Abstract:

We obtain the general solution and the stability of the functional equation ð ‘“ ( ð ‘¥ + 𠑦 + 𠑧 , ð ‘¢ + ð ‘£ + 𠑤 ) + ð ‘“ ( ð ‘¥ + 𠑦 − 𠑧 , ð ‘¢ + ð ‘£ + 𠑤 ) + 2 ð ‘“ ( ð ‘¥ , ð ‘¢ − 𠑤 ) + 2 ð ‘“ ( 𠑦 , ð ‘£ − 𠑤 ) = ð ‘“ ( ð ‘¥ + 𠑦 , ð ‘¢ + 𠑤 ) + ð ‘“ ( ð ‘¥ + 𠑦 , ð ‘£ + 𠑤 ) + ð ‘“ ( ð ‘¥ + 𠑧 , ð ‘¢ + 𠑤 ) + ð ‘“ ( ð ‘¥ − 𠑧 , ð ‘¢ + ð ‘£ − 𠑤 ) + ð ‘“ ( 𠑦 + 𠑧 , ð ‘£ + 𠑤 ) + ð ‘“ ( 𠑦 − 𠑧 , ð ‘¢ + ð ‘£ − 𠑤 ) . The function ð ‘“ ( ð ‘¥ , 𠑦 ) = ð ‘¥ 3 + ð ‘Ž ð ‘¥ + ð ‘ âˆ’ 𠑦 2 having level curves as elliptic curves is a solution of the above functional equation.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:135237

DOI: 10.1155/2008/135237

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