SciELO - Scientific Electronic Library Online

 
vol.41 issue3On fuzzy γµ-open sets in generalized fuzzy topological spacesNear-Zumkeller numbers author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • On index processCited by Google
  • Have no similar articlesSimilars in SciELO
  • On index processSimilars in Google

Share


Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

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.  http://dx.doi.org/10.22199/issn.0717-6279-4691.

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.

        · text in English     · English ( pdf )