TY - JOUR
TI - Cubic functional equations on restricted domains of lebesgue measure zero
AU - Choi, C.-K.
AU - Chung, J.
AU - Ju, Y.
AU - Rassias, J.
JO - CANADIAN MATHEMATICAL BULLETIN
PY - 2017
VL - 60
TODO - 1
SP - 95-103
PB - Canadian Mathematical Society
SN - 0008-4395
TODO - 10.4153/CMB-2016-041-4
TODO - null
TODO - 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.
ER -