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2008 A fixed point approach to the stability of a generalized Cauchy functional equation
Abbas Najati , Asghar Rahimi
Banach J. Math. Anal. 2(1): 105-112 (2008). DOI: 10.15352/bjma/1240336279

Abstract

We investigate the following generalized Cauchy functional equation \[ f(\alpha x+\beta y)=\alpha f(x)+\beta f( y) \] where $\alpha,\beta\in \Bbb{R}\setminus\{0\},$ and use a fixed point method to prove its generalized Hyers-Ulam-Rassias stability in Banach modules over a $C^*$-algebra.

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Abbas Najati . Asghar Rahimi. "A fixed point approach to the stability of a generalized Cauchy functional equation." Banach J. Math. Anal. 2 (1) 105 - 112, 2008. https://doi.org/10.15352/bjma/1240336279

Information

Published: 2008
First available in Project Euclid: 21 April 2009

zbMATH: 1143.39016
MathSciNet: MR2417527
Digital Object Identifier: 10.15352/bjma/1240336279

Subjects:
Primary: 39B72
Secondary: 47H09

Keywords: Banach module , C*-algebra , fixed point , generalized metric space , stability

Rights: Copyright © 2008 Tusi Mathematical Research Group

Vol.2 • No. 1 • 2008
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