Title: Hyers-Ulam-Rassias RNS Approximation of Euler-Lagrange-Type Additive Mappings
Abstract: Recently the generalized Hyers‐Ulam (or Hyers‐Ulam‐Rassias) stability of the following functional equation where r 1 , …, r m ∈ ℝ , proved in Banach modules over a unital C * ‐algebra. It was shown that if , r i , r j ≠ 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).