PM-空间中一类n变量混合型泛函方程的稳定性

Stability of a class of mixed functional equations with n variables in PM-space

利用差分算子的定义给出了一类新的n变量可加-二次混合型泛函方程,并通过对函数性态进行分类得到了其在实向量空间中的通解,同时利用不动点方法证明了该混合型泛函方程在PM-空间中具有Hyers-Ulam稳定性.

A new class of additive-quadratic hybrid functional equations of n variables was given by using the definition of difference operators.By categorizing the functional states,its general solution in real vector space was obtained,and the fixed-point method was used to prove that the hybrid functional equations have Hyers-Ulam stability in PM-space.