Generalized Multiquartic Mappings, Stability, and Nonstability - Abasalt Bodaghi (Journal of Mathematics)
In this article, a generalized form of n-quartic mappings is introduced. The structure of such mappings is studied, and in fact, it is shown that every multiquartic mapping can be described as an equation, namely, the (generalized) multiquartic functional equation. Moreover, by applying two fixed point techniques, some results corresponding to known stability outcomes including Hyers, Rassias, and Găvruţa stabilities are presented. Using a characterization result, an appropriate counterexample is supplied to invalidate the results in the case of singularity.