Stability of a Quartic Functional Equation in Restricted Domains

Abstract EN

Let X be a real normed space and Y a Banach space and f : X → Y .

We prove the Ulam-Hyers stability theorem for the quartic functional equation f ( 2 x + y ) + f ( 2 x - y ) - 4 f ( x + y ) - 4 f ( x - y ) - 24 f ( x ) + 6 f ( y ) = 0 in restricted domains.

As a consequence we consider a measure zero stability problem of the above inequality when f : R → Y .