Solution and two types of Ulam-Hyers stability of $n$-dimensional cubic-quartic functional equation in intuitionistic normed spaces

Abstract

In this paper, the authors investigate the generalized Ulam-Hyers stability of $n$ - dimensional cubic-quartic functional equation
$$
\begin{aligned}
f\left(\sum_{b=1}^{n-1} v_b+r v_n\right)+f\left(\sum_{b=1}^{n-1} v_b-r v_n\right)= & r^2\left[f\left(\sum_{b=1}^n v_b\right)+f\left(\sum_{b=1}^{n-1} v_b-v_n\right)\right] \\
& -2\left(r^2-1\right) f\left(\sum_{b=1}^{n-1} v_b\right)+\frac{2(r+1)}{r}\left[f\left(r v_n\right)-r^3 f\left(v_n\right)\right]
\end{aligned}
$$
where $r$ is a positive integer with $r \neq \pm 0,1$ in the setting of intuitionistic fuzzy normed spaces using direct and fixed point methods.