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.

Characterization, stability and hyperstability of multi-quadratic–cubic mappings

“…In other words, we reduce the system of n equations defining the multi-quadratic-cubic mappings to obtain a single functional equation. We also prove the generalized Hyers-Ulam stability and hyperstability for multiquadratic-cubic functional equations by using the fixed point method which was used for the first time by Brzdȩk in [12]; for more applications of this approach for the stability of multi-Cauchy-Jensen, multi-additive-quadratic, multi-cubic and multi-quartic mappings in Banach spaces see [2,3,10] and [8] respectively.…”

Characterization and stability analysis of advanced multi-quadratic functional equations

“…Indeed, we prove that every multi-quadratic mapping can be shown a single functional equation and vice versa (under some extra conditions). In addition, by using a fixed point theorem, we establish the Hyers-Ulam stability for the multi-quadratic functional equations; for more applications of this technique to prove the Hyers-Ulam stability of several variables mappings, we refer to [31][32][33][34][35][36], and [37].…”

Characterization and Stability of Multimixed Additive-Quartic Mappings: A Fixed Point Application

“…Bodaghi et al [4] (resp., [6]) provided a characterization of multicubic (resp., multiquartic) mappings, and they showed that every multicubic (resp., multiquartic) mapping can be shown a single functional equation and vice versa.…”