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2007 Hyers-Ulam-Rassias stability of a generalized Pexider functional equation
Belaid Bouikhalene, Ahmed Charifi, Elhoucien Elqorachi
Banach J. Math. Anal. 1(2): 176-185 (2007). DOI: 10.15352/bjma/1240336214


In this paper, we obtain the Hyers-Ulam-Rassias stability of the generalized Pexider functional equation $$ \sum_{k\in K} f(x+k\cdot y)=|K|g(x)+|K|h(y), \; x, y \in G ,$$ where $G$ is an abelian group, $K$ is a finite abelian subgroup of the group of automorphism of $G$.

The concept of Hyers-Ulam-Rassias stability originated from Th.M. Rassias' Stability Theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978), 297-300.


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Belaid Bouikhalene. Ahmed Charifi. Elhoucien Elqorachi. "Hyers-Ulam-Rassias stability of a generalized Pexider functional equation." Banach J. Math. Anal. 1 (2) 176 - 185, 2007.


Published: 2007
First available in Project Euclid: 21 April 2009

zbMATH: 1130.39022
MathSciNet: MR2366099
Digital Object Identifier: 10.15352/bjma/1240336214

Primary: 39B82
Secondary: 39B52‎

Keywords: group automorphism , Hyers-Ulam-Rassias stability , Jensen functional equation , quadratic functional equation

Rights: Copyright © 2007 Tusi Mathematical Research Group

Vol.1 • No. 2 • 2007
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