This paper introduces a new dimension of an additive functional equation and obtains its general solution. The main goal of this study is to examine the Ulam stability of this equation in IFN-spaces (intuitionistic fuzzy normed spaces) with the help of direct and fixed point approaches and 2-Banach spaces. Also, we use an appropriate counterexample to demonstrate that the stability of this equation fails in a particular case.

We propose a novel generalized quartic functional equation and investigate its Hyers–Ulam stability in modular spaces using a fixed point technique and the Fatou property in this paper.