Open AccessStability of generalized quadratic functional equation on a set of measure zero
Author(s) -
Youssef Aribou,
Hajira Dimou,
Abdellatif Chahbi,
Samir Kabbaj
Publication year - 2015
Publication title -
annales universitatis paedagogicae cracoviensis. studia mathematica
Language(s) - English
Resource type - Journals
eISSN - 2300-133X
pISSN - 2081-545X
DOI - 10.1515/aupcsm-2015-0011
Subject(s) - lebesgue measure , measure (data warehouse) , mathematics , zero (linguistics) , null set , stability (learning theory) , quadratic equation , functional equation , set (abstract data type) , mathematical analysis , lebesgue integration , space (punctuation) , pure mathematics , differential equation , computer science , geometry , linguistics , philosophy , database , machine learning , programming language , operating system
In this paper we prove the Hyers-Ulam stability of the following K-quadratic functional equation ∑ k ∈ K f(x+ k.y)= Lf(x)+ Lf(y), x,y ∈ E, where E is a real (or complex) vector space. This result was used to demonstrate the Hyers-Ulam stability on a set of Lebesgue measure zero for the same functional equation