Generalized Ulam-Hyers Stability of $n-$Dimensional AQCQ Functional Equation in Fuzzy Banach Spaces in Two Different Methods

Abstract

In this paper, the authors achieve the generalized Hyers-Ulam-stability of $n-$dimensional additive-quadratic-cubic-quartic functional equation
\begin{align*}
f\left(\sum_{k=1}^{n-1}x_k+2x_n\right)+f\left(\sum_{k=1}^{n-1}x_k-2x_n\right)&=4f\left(\sum_{k=1}^{n}x_k\right)+4f\left(\sum_{k=1}^{n-1}x_k-x_n\right)-6f\left(\sum_{k=1}^{n-1}x_k\right)\notag\\
&\quad+f(2x_n)+f(-2x_n)-4f(x_n)-4f(-x_n)
\end{align*}
in fuzzy Banach spaces using direct and fixed point methods.