A Functional Equation Originating from Elliptic Curves
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 functi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2008-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2008/135237 |