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

Authors

  • Rachid El Ghali Ibn Tofaïl University.
  • Samir Kabbaj Ibn Tofaïl University.

DOI:

https://doi.org/10.22199/issn.0717-6279-4691

Keywords:

bi-additive functional equation, Hyers-Ulam stability, functional equation, Baire category theorem, first category, Lebesgue measure

Abstract

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.

Author Biographies

Rachid El Ghali, Ibn Tofaïl University.

Dept. of Mathematics.

Samir Kabbaj, Ibn Tofaïl University.

Department of Mathematics.

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Published

2022-06-01

How to Cite

[1]
R. El Ghali and S. Kabbaj, “Stability problem in a set of Lebesgue measure zero of bi-additive functional equation”, Proyecciones (Antofagasta, On line), vol. 41, no. 3, pp. 751-764, Jun. 2022.

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