Nonlinear fuzzy stability of a functional equation related to a characterization of inner product spaces via fixed point technique
Abstract
Using the fixed point method, we prove some results concerning the stability of the functional equation
\begin{eqnarray*}
\sum^{2n}_{i=1}f(x_{i}-\frac{1}{2n}\sum^{2n}_{j=1}x_{j})=\sum^{2n}_{i=1}f(x_{i})-2n
f(\frac{1}{2n}\sum^{2n}_{i=1}x_{i})
\end{eqnarray*}
where $f$ is defined on a vector space and taking values in a fuzzy Banach space, which is said to be a functional equation related to a characterization of inner product spaces.
\begin{eqnarray*}
\sum^{2n}_{i=1}f(x_{i}-\frac{1}{2n}\sum^{2n}_{j=1}x_{j})=\sum^{2n}_{i=1}f(x_{i})-2n
f(\frac{1}{2n}\sum^{2n}_{i=1}x_{i})
\end{eqnarray*}
where $f$ is defined on a vector space and taking values in a fuzzy Banach space, which is said to be a functional equation related to a characterization of inner product spaces.
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