A functional equation originating from elliptic curves

作者：Park Won Gil; Bae Jae Hyeong^*

来源：Abstract and Applied Analysis, 2008, 135237.

DOI：10.1155/2008/135237

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) = x(3) + ax + b - y(2) having level curves as elliptic curves is a solution of the above functional equation.

• 出版日期2008