JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, v. 9, NO 6, Page. 4554-4562
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 inequality
kf(x + y) + f(x − y) − 2f(x) − 2h(y)k ≤ ,
in a set Ω ⊂ R
2 of Lebesgue measure m(Ω) = 0.
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