# On an equation characterizing multi-cubic mappings and its stability and hyperstability

## TL;DR

This paper investigates multi-cubic mappings, establishes a functional equation characterizing them, and applies fixed point methods to prove their Hyers-Ulam stability and hyperstability.

## Contribution

It introduces a functional equation for multi-cubic mappings and extends stability results, including hyperstability, using fixed point techniques.

## Key findings

- Multi-cubic mappings satisfy a specific functional equation.
- Hyers-Ulam stability is established for these mappings.
- Multi-cubic functional equations can be hyperstable.

## Abstract

In this paper, we introduce $n$-variables mappings which are cubic in each variable. We show that such mappings satisfy a functional equation. The main purpose is to extend the applications of a fixed point method to establish the Hyers-Ulam stability for the multi-cubic mappings. As a consequence, we prove that a multi-cubic functional equation can be hyperstable.