Stability problem in a set of Lebesgue measure zero of bi-additive functional equation

• El Ghali, Rachid ^[1] ; Kabbaj, Samir ^[1]
  1. [1] Université Ibn-Tofail

     Université Ibn-Tofail

     Kenitra, Marruecos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 3, 2022, págs. 751-764
• Idioma: inglés
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• Resumen

  • 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.