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Proyecciones (Antofagasta)

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GHALI, Rachid El  and  KABBAJ, Samir. Stability problem in a set of Lebesgue measure zero of bi-additive functional equation. Proyecciones (Antofagasta) [online]. 2022, vol.41, n.3, pp.751-764. ISSN 0716-0917.

Let X be a vector space and Y be a Banach space. Our aim in this paper is to investigate the Hyers-Ulam stability problem of the following bi-additive 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.

Keywords : bi-additive functional equation; Hyers-Ulam stability; functional equation; Baire category theorem; first category; Lebesgue measure.

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