Operatorial approach to the non-Archimedean stability of a Pexider K-quadratic functional equation

Operatorial approach to the non-Archimedean stability of a Pexider K-quadratic functional equation

We use the operatorial approach to obtain, in non-Archimedean spaces, the Hyers–Ulam stability of the Pexider K-quadratic functional equation∑k∈Kf(x+k·y)=κg(x)+κh(y),x,y∈E,where f,g,h:E→F are applications and K is a finite subgroup of the group of automorphisms of E and κ is its order.

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Veröffentlicht in:Arab journal of mathematical sciences 2015-01, Vol.21 (1), p.67-83
Hauptverfasser: Chahbi, A.B., Charifi, A., Bouikhalene, B., Kabbaj, S.
Format: Artikel
Sprache:eng
Schlagworte:
Group automorphisms
Jensen functional equation
K-quadratic functional equation
Non-Archimedean Hyers–Ulam stability
Pexider functional equation
Quadratic functional equation
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Zusammenfassung:We use the operatorial approach to obtain, in non-Archimedean spaces, the Hyers–Ulam stability of the Pexider K-quadratic functional equation∑k∈Kf(x+k·y)=κg(x)+κh(y),x,y∈E,where f,g,h:E→F are applications and K is a finite subgroup of the group of automorphisms of E and κ is its order.
ISSN:1319-5166
DOI:10.1016/j.ajmsc.2014.01.001