Stability of generalized cubic- and quartic-type functional equations in the setting of non-Archimedean spaces

In the field of functional equations and their solutions, Ulam's stability is an essential concept. This theory examines whether the function approximating a certain functional equation is close to the function that exactly satisfies it. A broader extension of the stability concept is generalized Hyers–Ulam stability. Classifying, analysing and solving functional equations across multiple spaces are made easier by using this. In this investigation, we examine the generalized Hyers–Ulam stability of generalized cubic- and quartic-type functional equations of the form: (Formula presented.) and (Formula presented.) in setting of non-Archimedean (n-A) normed spaces by using distinguished Hyers direct method. Also, we provide a graphical representation of an approximate solution and how it differs from an exact solution for both equations. Furthermore, we present counterexamples that demonstrate the failure case of stability.