Intuitionistic Fuzzy Stability of an Finite Dimensional Cubic Functional Equation

Abstract

In the current work, the intuitionistic fuzzy version of Hypers-Ulam stability for a k-dimensional cubic functional equation

$$\begin{aligned} \begin{aligned}&\sum _{j=1}^{k}f\left[ \sum _{i(\ne j)=1}^{k}n^{i}x_{i}-n^{j}x_{j}\right] +(6-k)f\left( \sum _{i=1}^{k}n^{i}x_{i}\right) \\ =&4\left[ \sum _{j=1}^{k}\sum _{i(<j)=1}^{k}f(n^{i}x_{i}+n^{j}x_{j})-(k-2)\sum _{i=1}^{k}f(n^{i}x_{i})\right] \end{aligned} \end{aligned}$$

by applying a direct and fixed point methods is investigated. This way shows that some fixed points of a suitable operator can be a cubic mapping.