Stability Analysis of Quartic Functional Equation in Intuitionistic Fuzzy and 2-Normed Frameworks

In this research, we study the Hyers-Ulam stability of a finite-dimensional quartic functional equation using two generalized analytical frameworks: intuitionistic fuzzy normed spaces (IFN-spaces) and 2-Banach spaces. The study employs two separate approaches: the direct method and the fixed point methodology, which provide complementary insights on stability behavior. By setting appropriate control conditions defined by sums and products of powers of norms, we demonstrate the existence and uniqueness of a quartic mapping that approximates the given functional equation. The results show that, under the right contractive conditions, approximate solutions converge to an accurate quartic function. Several corollaries are developed to demonstrate how stability bounds are explicitly dependent on the form of the control function. These findings broaden the application of classical Hyers-Ulam stability theory to nonlinear contexts and help to advance stability analysis in fuzzy and multi-normed functional frameworks.