Approximation of a Cauchy-Jensen Additive Functional Equation in Non-Archimedean Normed Spaces

Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f(∑i=1pxi+∑j=1qyj+2∑k=1dzk2)=∑i=1pf(xi)+∑j=1qf(yj)+∑d=1df(zk), where p, q, d are integers greater than 1, in non-Archimedean normed spaces.