Cauchy-三次函数方程及其Hyers—Ulam稳定性

On a Cauchy-Cubic Functional Equation and Its Hyers-Ulam Stability

给出Cauchy-三次函数方程f(x_1+x_2,2y_1+y_2)+f(x_1+x_2,2y_1-y_2)=2f(x_1,y_1+y_2)+2f(x_1,y_1-y_2)+12f(x_1,y_1)+2f(x_2,y_1+y_2)+2f(x_2,y_1-y_2)+12f(x_2,y_1)的一般解,并用直接方法和不动点方法研究它在Banach空间上的HyersUlam稳定性及模糊稳定性.

We obtain the general solution and the generalized Hyers-Ulam stability of the Cauchy-cubic functional equation f(x_1+x_2,2y_1+y_2)+f(x_1+x_2,2y_1-y_2)=2f(x_1,y_1+y_2)+2f(x_1,y_1-y_2)+12f(x_1,y_1)+2f(x_2,y_1+y_2)+2f(x_2,y_1-y_2)+12f(x_2,y_1)in Banach space and fuzzy Banach space using the direct method and the fixed point method,respectively.