Hyers–Ulam–Rassias stability of Cauchy–Jensen functional equation in RN-spaces

Using the fixed point and direct methods, we prove the Hyers–Ulam stability of the following Cauchy–Jensen functional equation. 2f(∑pi=1xi+∑qj=1yj2+∑k=1dzk)=∑i=1pf(xi)+∑j=1qf(yj)+2∑k=1df(zk) where p,q,d are positive integers, in random normed spaces.