The aim of this article is to extend the applications of a fixed point method to provide the intuitionistic fuzzy versions of Hyers-Ulam stability for the generalized forms of cubic and quartic functional equations. This way shows that the concept of

The oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation f(2x + y) + f(2x − y) = 4f(x + y) + 4f(x − y) + 24f(x) − 6f(y) is called a quartic functional equation, all of its solution is said to be a quartic function. In the current paper, the Hyers‐Ulam stability and the superstability for quartic functional equations are established by using the fixed‐point alternative theorem.

In this article, we introduce the generalized multi-quadratic mappings and then describe them as a equation. As a special case of such mappings, we study the Hyers-Ulam stability of multi-quadratic mappings in non-Archimedean spaces by applying a fixed point theorem. Moreover, we prove that such mappings can be hyperstable.

In the current paper, we study the stability and the superstability of ∗-derivations associated with the Cauchy functional equation and the Jensen functional equation. We also prove the stability and the superstability of Jordan ∗-derivations on Banach ∗-algebras.