Stability of $n-$ Dimensional Additive Functional Equation in Fuzzy Normed Spaces

Abstract

In this paper, the authors investigate the generalized Hyers-Ulam-stability of new $n-$ dimensional additive functional equation 
\[
\sum_{j=1}^n f\left(-x_j+\sum_{1\leq i\leq n, i\neq j} x_{i}\right)=(n-2)\sum_{j=1}^n f(x_j)
\]
in fuzzy normed space using direct and fixed point approach.