Stability of generalized quadratic functional equation on a set of measure zero

Youssef Aribou, Hajira Dimou, Abdellatif Chahbi, Samir Kabbaj

Abstract


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.

Keywords


group automorphisms; Jensen functional equation; quadratic functional equation; K -quadratic functional equation; Pexider functional equation; Hyers-Ulam stability

Mathematics Subject Classification (2010)


Primary 39B82; Secondary 39B52;

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