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.
Citation
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
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