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Recently the generalized Hyers-Ulam (or Hyers-Ulam-Rassias) stability of the following functional equation ∑j=1mf(-rjxj+∑1≤i≤m,i≠jrixi)+2∑i=1mrif(xi)=mf(∑i=1mrixi) where r1,…,rm∈ℝ, proved in Banach modules over a unital C*-algebra. It was shown that if ∑i=1mri≠0, ri, rj≠0 for some 1≤i<j≤m and a mapping f:X→Y satisfies the above mentioned functional equation then the mapping f:X→Y is Cauchy additive. In this paper we prove the Hyers-Ulam-Rassias stability of the above mentioned functional equation in random normed spaces (briefly RNS).

Hyers-Ulam-Rassias RNS Approximation of Euler-Lagrange-Type Additive Mappings