Approximation of Jordan Homomorphisms in Jordan Banach Algebras

In this paper, we investigate the generalized Hyers-Ulam stability of Jordan homomorphisms in Jordan Banach algebras for the functional equation \begin{align*} \sum_{k=2}^n \sum_{i_1=2}^k\sum_{i_2=i_{1}+1}^{k+1}\cdots\sum_{i_n-k+1=i_{n-k}+1}^n f\left(\sum_{i=1,i \not=i_{1},\cdots ,i_{n-k+1}}^n x_{i}-\sum_{r=1}^{n-k+1} x_{i_{r}}\right) + \ \\ f\left(\sum_{i=1}^{n}x_{i}\right)-2^{n-1} f(x_{1}) =0,\ \ \ \ \ \ \ \ \ \ \ \ \end{align*} where $n$ is an integer greater than 1.