Abstract

Recently the generalized Hyers‐Ulam (or Hyers‐Ulam‐Rassias) stability of the following functional equation where r1, …, rm ∈ ℝ, proved in Banach modules over a unital C*‐algebra. It was shown that if , 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).

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