Stability problem in a set of Lebesgue measure zero of biadditive functional equation
DOI:
https://doi.org/10.22199/issn.071762794691Keywords:
biadditive functional equation, HyersUlam stability, functional equation, Baire category theorem, first category, Lebesgue measureAbstract
Let X be a vector space and Y be a Banach space. Our aim in this paper is to investigate the HyersUlam stability problem of the following biadditive functional equation
f(x + y, s − t) + f(x − y, s + t)=2f(x, s) − 2f(y, t), x, y, s, t ∈ X,
where f : X × X → Y . As a consequence, we discuss the stability of the considered functional equation in a restricted domain and in the set of Lebesgue measure zero.
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