Commun. Korean Math. Soc. 2013; 28(2): 319-333
Printed April 1, 2013
https://doi.org/10.4134/CKMS.2013.28.2.319
Copyright © The Korean Mathematical Society.
Fridoun Moradlou
Sahand University of Technology
Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-\linebreak Banach spaces: \begin{equation*} \sum_{1 \le i < j \le n}f\Big(\frac{r_ix_i +r_jx_j}{k}\Big) = \frac{n-1}{k}\sum_{i=1}^{n}r_if(x_i). \end{equation*}
Keywords: fixed point method, Hyers--Ulam--Rassias stability, multi-Banach spaces, Euler-Lagrange mapping
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