Cubic Functional Equations on Restricted Domains of Lebesgue Measure Zero

Abstract

AbstractLet X be a real normed space, Y a Banach space, and f : X → Y. We prove theUlam–Hyers stability theorem for the cubic functional equationin restricted domains. As an application we consider a measure zero stability problem of the inequalityfor all (x, y) in Γ ⸦ ℝ2 of Lebesgue measure 0.