Multiquartic functional equations

Abstract

In this paper, we study n-variable mappings that are quartic in each variable. We show that the conditions defining such mappings can be unified in a single functional equation. Furthermore, we apply an alternative fixed point method to prove the Hyers-Ulam stability for the multiquartic functional equations in the normed spaces. We also prove that under some mild conditions, every approximately multiquartic mapping is a multiquartic mapping.