Abstract
We obtain the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary -norms .
Highlights
The stability problem of functional equations originated from a question of Ulam 1 in 1940, concerning the stability of group homomorphisms
We suppose that X is a real linear space, Y, μ, T is a complete RN-space, and f : X → Y is a function with f 0 0 for which there is ρ : X × X → D ρ x, y denoted by ρx,y with the property μf x 2y f x−2y −4 fxyfx−y 24f y 6f x −3f 2y t ≥ ρx,y t
We show that C is a cubic map
Summary
The stability problem of functional equations originated from a question of Ulam 1 in 1940, concerning the stability of group homomorphisms. Jun and Kim 13 introduced the following cubic functional equation: f 2x y f 2x − y 2f x y 2f x − y 12f x They proved that a function f between real vector spaces X and Y is a solution of 1.4 if and only if there exists a unique symmetric multiadditive function Q : X × X × X × X → Y
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