a functional equation originating from elliptic curves

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ID: 187603
2008
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Abstract
We obtain the general solution and the stability of the functional equation ๐‘“(๐‘ฅ+๐‘ฆ+๐‘ง,๐‘ข+๐‘ฃ+๐‘ค)+๐‘“(๐‘ฅ+๐‘ฆโˆ’๐‘ง,๐‘ข+๐‘ฃ+๐‘ค)+2๐‘“(๐‘ฅ,๐‘ขโˆ’๐‘ค)+2๐‘“(๐‘ฆ,๐‘ฃโˆ’๐‘ค)=๐‘“(๐‘ฅ+๐‘ฆ,๐‘ข+๐‘ค)+๐‘“(๐‘ฅ+๐‘ฆ,๐‘ฃ+๐‘ค)+๐‘“(๐‘ฅ+๐‘ง,๐‘ข+๐‘ค)+๐‘“(๐‘ฅโˆ’๐‘ง,๐‘ข+๐‘ฃโˆ’๐‘ค)+๐‘“(๐‘ฆ+๐‘ง,๐‘ฃ+๐‘ค)+๐‘“(๐‘ฆโˆ’๐‘ง,๐‘ข+๐‘ฃโˆ’๐‘ค). The function ๐‘“(๐‘ฅ,๐‘ฆ)=๐‘ฅ3+๐‘Ž๐‘ฅ+๐‘โˆ’๐‘ฆ2 having level curves as elliptic curves is a solution of the above functional equation.
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park2008abstracta Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Won-Gil Park;Jae-Hyeong Bae
Journal science and technology of advanced materials
Year 2008
DOI
10.1155/2008/135237
URL
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