On an equation characterizing multi-quartic mappings and its stability

Document Type : Research Paper


1 Department of Mathematics, Tehran North Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran


In this paper, we define and investigate the mappings of several variables which are quartic in each variable. We show that such mappings can be unified as an equation, say the multi-quartic functional equation. We also establish the Hyers-Ulam stability of a such functional equation by a fixed point theorem in non-Archimedean normed spaces. Moreover, we generalize some known stability and hyperstability results.