Approximately generalized additive functions in several variables via fixed point method
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Abstract:
In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability in random normed spaces, in non-Archimedean spaces and also in $p$-Banach spaces and finally the stability via fixed point method for a functional equationbegin{align*}&D_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1, ineq i_{1},...,i_{m-k+1} } x_{i}-sum^{m-k+1}_{ r=1} x_{i_{r}})\& hspace {2.8cm}+f(sum^{m}_{ i=1} x_{i})-2^{m-1} f(x_{1})=0end{align*}where $m geq 2$ is an integer number.
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Journal title
volume 7 issue 1
pages 167- 181
publication date 2016-03-19
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