Stability of Pexiderized quadratic functional equation on a set of measure zero

Abstract

Let R be the set of real numbers and Y a Banach space. We prove the Hyers-Ulam stability theorem when f, h : R → Y satisfy the following Pexider quadratic inequalityin a set Ω ⊂ R 2 of Lebesgue measure m(Ω) = 0. c 2016 All rights reserved.