@article{3024644,
    title = "Cubic functional equations on restricted domains of lebesgue measure zero",
    author = "Choi, C.-K. and Chung, J. and Ju, Y. and Rassias, J.",
    journal = "CANADIAN MATHEMATICAL BULLETIN",
    year = "2017",
    volume = "60",
    number = "1",
    pages = "95-103",
    publisher = "Canadian Mathematical Society",
    issn = "0008-4395",
    doi = "10.4153/CMB-2016-041-4",
    abstract = "Let X be a real normed space, Y a Banach space, and f f X → Y. We prove the Ulam-Hyers stability theorem for the cubic functional equation f (2x + y) + f (2x - y) - 2 f (x + y) - 2 f (x - y) - 12 f (x) = 0 in restricted domains. As an application we consider a measure zero stability problem of the inequality ∥ f (2x + y) + f (2x - y) - 2 f (x + y) - 2 f (x - y) - 12 f (x) ∥ ≤ ∈ for all (x, y) in Γ R2 of Lebesgue measure 0. © 2016 Canadian Mathematical Society."
}