Stability of a quartic functional equation in restricted domains (Q739904)

Summary: Let \(X\) be a real normed space and \(Y\) a Banach space and \(f : X \to Y\). We prove the Ulam-Hyers stability theorem for the quartic functional equation \(f(2 x + y) + f(2 x - y) - 4 f(x + y) - 4 f(x - y) - 24 f(x) + 6 f(y) = 0\) in restricted domains. As a consequence we consider a measure zero stability problem of the above inequality when \(f : \mathbb{R} \to Y\).