Measure zero stability problem of a generalized quadratic functional equation

Let X be a normed space, Y be a Banach space and f , g : X → Y . In this paper, we investigate the Hyers–Ulam stability theorem for the generalized quadratic functional equation f ( k x + y ) + f ( k x - y ) = 2 k 2 g ( x ) + 2 f ( y ) in a set Ω ⊂ X × X , where k is a positive integer. By the Baire category theorem, we derive some consequences of our main result.