On generalized Hyers-Ulam stability of an $n$-dimensional additive functional equation

Abstract

The paper investigated the following generalized $n$-dimensional additive functional equation in fuzzy normed space $$\sum\limits_{1\leq i<j<k<l\leq n}f(x_i+x_j+x_k+x_l)=\left(\dfrac{n^3-6n^2+11n-6}{6}\right)\sum\limits_{i=1}^{n}{ f(x_i)},$$
where $n\in \mathbb{N}-\{0,1,2,3\}$. The stability of obtained general solution has been investigated with the help of generalized Hyers-Ulam method associated with direct and fixed point approaches.