On the Stability of Multicubic-Quartic and Multimixed Cubic-Quartic Mappings

Abstract

In this paper, we define the multi-cubic-quartic and the multi-mixed
cubic-quartic mappings and characterize them. In other word, we
unify the system of functional equations defining a multi-mixed
cubic-quartic (multi-cubic-quartic) mapping to a single equation
namely, the multi-mixed cubic-quartic (multi-cubic-quartic)
functional equation. Moreover, by using a fixed point theorem, we
study the generalized Hyers-Ulam stability of multi-mixed
cubic-quartic functional equations in non-Archimedean normed spaces.
As a corollary, we show that every multi-mixed cubic-quartic mapping
under some mild conditions can be hyperstable.