On the stability of multicubic-quartic and multimixed cubic-quartic mappings

Abstract

In this paper, we define the multicubic-quartic and the multimixed cubic-quartic mappings and characterize them. In other words, we unify the system of functional equations defining a multimixed cubic-quartic (resp., multicubic-quartic) mapping to a single equation, namely, the multimixed cubic-quartic (resp., multicubic-quartic) functional equation. We also show that under what conditions a multimixed cubic-quartic mapping can be multicubic, multiquartic and multicubic-quartic. Moreover, by using a fixed point theorem, we study the generalized Hyers-Ulam stability of multimixed cubic-quartic functional equations in non-Archimedean normed spaces. As a corollary, we show that every multimixed cubicquartic mapping under some mild conditions can be hyperstable. Lastly, we present a non-stable example for the multiquartic mappings.